Simulation of Winter Wheat Growth Dynamics and Optimization of Water and Nitrogen Application Systems Based on the Aquacrop Model

Abstract

Winter wheat is the main grain crop in the Yellow River Basin, and optimizing water and nitrogen management can not only improve the yield, but also reduce water and fertilizer waste and environmental pollution. Using two years of winter wheat field trials, the Aquacrop model was calibrated and validated, and 36 different water and nitrogen application scenarios were simulated and analyzed. Among them, the field trials were divided into three N application levels, and three lower limits of water control. The results showed that: (1) the model has good applicability to simulate the growth process of winter wheat in the Yellow River Basin. (2) At a constant level of irrigation or nitrogen application, crop yield initially increased and subsequently decreased with the enhancement of either irrigation or nitrogen application. Finally, through response surface analysis of regression equations, the recommended irrigation volume was determined to be between 296 and 303 mm, and the fertilizer application rate was set between 229 and 261 kg/ha. At these levels, the PFP could achieve over 60% of its maximum. This research provides a theoretical basis for the water-saving, fertilizer-saving and high-yield water and fertilizer management system of winter wheat in the irrigated area of the Yellow River Basin.

1. Introduction

The irrigation area of the Yellow River Basin holds a pivotal role as a grain production base in China, with winter wheat being the primary food crop cultivated in this region. Ensuring high crop yields within this irrigation district is critically significant for safeguarding China’s food security [1]. Meng Zhaogang et al. systematically studied the coupling effect of water and fertilizer between the upper and lower crops in the one-year two-crop system of winter wheat and summer maize in the irrigation area of the Yellow River Basin, and put forward the water and fertilizer optimization scheme under different decision-making objectives [2]. Currently, a notable challenge facing China’s agricultural production is the scarcity of water resources, coupled with low water and fertilizer utilization efficiency [3]. Two principal factors contribute to this inefficiency: firstly, the prevalent irrigation methodology, with flood irrigation being the predominant choice in China’s irrigation zones. This method leads to a considerable waste of water resources and loss of soil fertility. Secondly, the excessive application of fertilizers causes the fertilizer waste and an increase in pest infestations and diseases, which ultimately hinder crop yield. Therefore, achieving both high and stable yields while ensuring rational utilization of water and fertilizers has continually been a direction of research for a number of researchers [4]. Within the irrigated area of the Yellow River Basin, the total availability of water resources is markedly limited. The water allocation from the Yellow River often falls short of meeting the irrigation requirements, especially during dry seasons. Concurrently, a gradual decline in soil fertility adversely affects both the enhancement of agricultural yield and the sustainable advancement of agriculture. Therefore, optimizing the water and nitrogen management regimes emerges as a paramount agenda for enhancing agricultural development in the irrigation area of the Yellow River Basin [5].

The exploration of optimal irrigation and fertilization strategies through field trials can be time-consuming and susceptible to external influences [6] hence, employing crop models to simulate crop growth has evolved as a vital tool in modern agriculture. Currently, prevalent crop models include DSSAT, WOFOST, and AquaCrop, among others. Notably, by focusing on water use efficiency (WUE), AquaCrop has the advantages of requiring fewer input parameters, and having a simple and intuitive operation interface [7,8]. Numerous researchers have utilized the AquaCrop model to simulate crop growth across various global regions, thereby evaluating its applicability. For instance, Farahani et al. [9] calibrated parameters suitable for simulating cotton yield in the Mediterranean region, establishing a foundation for future applications of this model in the area. Similarly, Araya et al. [10] demonstrated the model’s efficacy in simulating the aboveground biomass and yield of barley under varying planting dates. Toumi et al. [11] employed the model to simulate the canopy cover and soil moisture content of winter wheat, validating the AquaCrop model’s feasibility in capturing the growth dynamics of winter wheat throughout its lifecycle. Andarzian et al. [12] demonstrated, based on simulated data for winter wheat in southern Iran, that under normal precipitation conditions, the AquaCrop model can accurately predict the pattern of soil moisture change.

Furthermore, many studies have been conducted to explore the effects of distinct climates on crop yields using AquaCrop model. At present, in China, several scholars have applied the Aquacrop model to simulate crop growth in different regions and evaluated the applicability of the model: He et al. [13] examined the impacts on tobacco yield in Yunnan province, showcasing high simulation accuracy. Ni et al. [14] evaluated the suitability of summer maize production in the Loess Plateau area, which is greatly beneficial for simulating water optimization management of summer maize in this region. Pan et al. [15] applied the model to simulate maize yield in northwest China employing full-film double-furrow sowing technology and concluded the model’s suitability for simulating local dry farming. Additional studies by Meng et al. [16] and Du et al. [17] successfully simulated the growth and yield of winter wheat in Hebei province of China, achieving high accuracy in simulation results. Zhu et al. [18] explored alternating fresh and saline irrigation methods for winter wheat during different fertility periods, calibrating crop growth and yield accordingly. Cui et al. [19] utilized the one factor at a time (OTA) method to conduct a sensitivity analysis of model parameters, then optimized the sensitive parameters, concluding that the calibrated model could accurately simulate corn and soybean yields in northeast China.

Moreover, the AquaCrop model has been employed to simulate the growth and yield of various crops such as corn [20,21], soybean [22] peanut [23], and rapeseed [24] all achieving high accuracy. Some researchers have extended the model’s application to crop economic efficiency analysis and evaluation [25] and irrigation regime optimization [26,27,28,29], achieving favorable outcomes. Overall, the AquaCrop model, post-parameter calibration, exhibits substantial applicability to different crops and demonstrates higher simulation accuracy compared to other models [30].

In this study, we selected winter wheat in the irrigation area of the Yellow River Basin as the research subject to evaluate the applicability of the AquaCrop model. Experimental treatments were established with varying irrigation water and amounts of nitrogen applied, over a span of two years, to gather field test data and corresponding data analysis results. Subsequently, the AquaCrop model was calibrated and validated, employing the collected experimental data. The calibrated model was then utilized to perform scenario simulations of winter wheat irrigation during different fertility periods to determine the optimum irrigation period for enhancing winter wheat fertility. The experimental data were fitted to the water–fertilizer coupling regression equation [31], and through this equation, a response surface map illustrating the effects of water and fertilizer on yield, WUE, and fertilizer partial factor productivity (PFP) was generated [32]. This visual representation provides an intuitive and comprehensive understanding of the impacts of varying irrigation volumes and fertilizer application rate on crop growth, as well as the overall trend of water–fertilizer coupling. By doing so, we aimed to obtain the optimal irrigation volume and fertilizer application rate for winter wheat in the irrigation area of the Yellow River Basin, to ensure high yield while conserving water and fertilizer resources. Our investigation not only provides a reference for the applicability of the AquaCrop model in the irrigation area of the Yellow River Basin, but also highlights the importance of optimizing water and nitrogen use. Through the integration of scenario simulations, we can ensure a higher yield of winter wheat in the region, improve the effectiveness of water and nitrogen utilization, mitigate soil deterioration, and reduce wasteful water use.

2. Materials and Methods

2.1. Overview of the Experimental Area

The study was conducted at the Experimental Field for Efficient Water Use in Agriculture, situated within the Longzi Lake Campus of the North China University of Water Resources and Hydropower, Zhengzhou. This location lies in the heart of the Central China Plain with the geographic coordinates 34.78° N latitude and 113.76° E longitude, at an elevation of 110 m above sea level. The local climate is characterized by a warm temperate continental monsoon climate with an average annual temperature of approximately 14.5 °C. The region receives an average annual precipitation of 637.1 mm, enjoys an average sunshine duration of 6.57 h per day, and experiences a frost-free period extending over 220 days. The experimental site features flat terrain with clay loam being the predominant soil type.

The winter wheat cultivation cycle in this region spans from planting in October of one year to harvesting in June of the following year. Accordingly, the experimental periods for this study were specified as October 2021 to June 2022 and October 2022 to June 2023. The precise location of the experimental site is depicted in Figure 1.

2.2. Experimental Design

In this study, the amounts of irrigation and fertilizer application were determined by the climatic conditions of the Yellow River Irrigation District. In addition, a study on the optimal allocation of water and nitrogen for winter wheat in north China based on the quantification of crop water-fertilizer coupling types was conducted [33]. Three levels of nitrogen application were established: N1 (120 kg/ha), N2 (220 kg/ha), and N3 (320 kg/ha). Concurrently, three distinct lower water control thresholds were designated at each N application level: W1 (60%θ_f), W2 (70%θ_f), and W3 (80%θ_f), where θ_f represents the field water holding capacity. For each treatment, nitrogen application was divided into a base fertilizer and two top-dressing fertilizations (base fertilizer for the first basic application and two surface applications for the two supplementary applications). The base fertilizer application was consistent at 67.5 kg/ha for all treatments, utilizing a ternary compound fertilizer (comprising 60 kg/ha of N, 60 kg/ha of K₂O, and 60 kg/ha of P₂O₅). The top-dressing fertilizer utilized was urea with a nitrogen content of 46.3%. The timings for top-dressing fertilizations were during the re-greening (returning-green stage) and tasseling (heading stage) periods of winter wheat, respectively [34].

Irrigation treatments were conducted according to the targeted soil moisture content within the wet layer during each fertility period, initiating irrigation whenever the soil moisture descended below the lower threshold of the targeted soil moisture content. The irrigation quota for winter wheat was set at a fixed 45 mm, and Jimai 22 was chosen as the seed variety. Conventional border irrigation was employed for the field experiments, with each plot measuring 10 m × 1.5 m. To ensure experimental accuracy, a buffer zone of 1.5 m width was established between adjacent plots.

Table 1. Water and fertilizer treatment configurations.

Treatment	Water Control Level	Number of Irrigations	Total Irrigation (mm)	Irrigation Quota (mm)	Nitrogen Application (kg/ha)	Base Fertilizer (kg/ha)	Top-Dressing Fertilizer (kg/ha)
W1N1	60%θf	4	45	4 × 45	67.5 + 52.5	67.5	52.5
W1N2	60%θf				67.5 + 152.5		152.5
W1N3	60%θf				67.5 + 252.5		252.5
W2N1	70%θf	6		6 × 45	67.5 + 52.5		52.5
W2N2	70%θf				67.5 + 152.5		152.5
W2N3	70%θf				67.5 + 252.5		252.5
W3N1	80%θf	9		9 × 45	67.5 + 52.5		52.5
W3N2	80%θf				67.5 + 152.5		152.5
W3N3	80%θf				67.5 + 252.5		252.5

outlines the specific water and fertilizer treatment configurations for the experimental plots:

2.3. Assessment Indicators and Methods

2.3.1. Aboveground Biomass and Yield

(1)

Aboveground biomass

The aboveground biomass was assessed every 10 days following the overwintering phase of winter wheat. In each treatment, five plants were selected for measurement. Plants were cut at ground level, and the aboveground parts were initially placed in a drying oven at 105 °C for 30 min to halt the greening process. The samples were then kept in the oven and dried at 75 °C until a constant mass was achieved.

(2)

Yield

The yield of winter wheat was calculated by multiplying the number of spikes per unit area, the number of grains per spike, and the mass of 1000 grains at harvest. The effective number of spikes within a 1 m² plot was determined. In each treatment, five representative plants were chosen, and the number of grains per spike on each plant was counted. Additionally, a set of 1000 wheat seeds harvested randomly was weighed to obtain the thousand-grain mass value.

2.3.2. Canopy Cover

The canopy cover of winter wheat during its reproductive period can be derived from the leaf area index (LAI) values. These LAI values were acquired using the values of several measured parameters shown in Equation (1) [17]:

$$LAI=0.75\times \rho \times \left(\frac{{\displaystyle \sum _{i=1}^m{\displaystyle \sum _{i=1}^n\left(L_{ij}\times B_{ij}\right)}}}{m}\right)$$

(1)

where m is the number of winter wheat plants per unit area; ρ is the planting density; L_ij and B_ij are the length and the width (at the widest part) of the leaf blade (in mm), respectively; n is the number of leaves on the selected plant; 0.75 is the correction coefficient.

Canopy cover was then calculated from the derived LAI value, as shown in Equation (2):

$$CC=1-{\exp }^{\left(-0.65\times LAI\right)}$$

(2)

2.3.3. Soil Water Content

The soil water content was monitored throughout the reproductive cycle of winter wheat using the time domain reflectometry with intelligent microelements (TRIME) method [35]. The TRIME method combines the proven principles of time domain reflectometry (TDR) with modern electronics and software algorithms to provide a robust tool for measuring soil water content. Measurements were conducted every 10 days following the overwintering phase. Prior to the commencement of the experiment, the TRIME probes were calibrated using the drying method. Measurements were obtained at a depth of 100 cm and at intervals of 20 cm.

2.3.4. WUE and Fertilizer PFP

The WUE is a critical metric that reflects the effectiveness of water utilization in crop production. It is calculated using the following formula [33]:

$$WUE=Y/ET$$

(3)

where Y stands for the yield (kg/ha); ET is the crop water consumption (mm), which can be calculated in the following equation:

$$ET=P+U+I-R-D-\Delta W$$

(4)

where P is the rainfall during the reproductive period (mm); U is the groundwater recharge (mm); I is the irrigation volume during the reproductive period (mm); D is the deep seepage (mm); R is the surface runoff (mm); and $\Delta W$ represents the change in soil moisture from the beginning to the end of the experiment (mm). According to the actual measurements, there was no significant change in the soil moisture content at a depth of 1 m in the experimental area. Additionally, given the deep groundwater level and relatively flat terrain in the experimental area, the terms U, D, and R in the formula can be neglected.

The expression for calculating fertilizer PFP is represented as follows:

$$PFP=Y/T$$

(5)

where Y is the yield (kg/ha); and T is the total amount of fertilizer applied during the reproductive period (kg/ha).

3. Results

3.1. Model Fundamentals

AquaCrop is a water-driven, daily timestep, crop model issued by the Food and Agriculture Organization of the United Nations (FAO) in 2009, with the aim of achieving an optimal balance between simplicity, accuracy, and robustness. To foster its utilization, AquaCrop is configured to require few parameters and intuitive input data that are either readily accessible or obtainable through straightforward measurements.

The operation principle of the AquaCrop model was elucidated comprehensively by Raes et al. [35] and Steduto et al. [36], encompassing the following principal simulation aspects: (1) simulation of crop canopy development; (2) simulation of crop transpiration; (3) simulation of crop aboveground biomass growth; (4) simulation of crop yields. The main equations are given as:

$$Y=B\times HI$$

(6)

$$B=WP*\times {\displaystyle \sum T_r}$$

(7)

where Y is the winter wheat yield (kg/ha); B is the aboveground biomass (kg/ha); HI is the winter wheat harvest index (%); WP* is the standardized water productivity (g/m²); and T_r is the crop transpiration (mm).

AquaCrop model adopts a semi-quantitative approach to illustrate the effects of fertilizer stress on crop growth without explicitly addressing nutrient cycling and balancing [30]. The model incorporates a scaling factor, B_rel, relative to the aboveground biomass that can be obtained under conditions without fertilizer and water stress, as expressed in Equation (8).

$$B_{rel}=\frac{B_{str}}{B_{ref}}\times 100\%$$

(8)

where B_str is the aboveground biomass (t/ha) in the absence of both fertilizer and water stress; B_ref is the aboveground biomass (t/ha) under fertilizer stress but devoid of water stress.

To investigate the impact of fertilizer stress on crop growth, four fertilizer stress coefficients were incorporated in the model: canopy expansion stress coefficient, maximum canopy cover, canopy decay stress coefficient, and biomass water productivity. This corresponded to the reduced maximum canopy cover, the decrease in canopy growth coefficient, the average canopy reduction, and the standardized crop water productivity reduction within the parameter calibration results as seen in

Table 2. Fertilizer stress parameters and their calibration values.

Nitrogen Treatment	Parameter Calibration Values			Parameter Calibration Results
	Relative Biomass Brel (%)	Maximum Canopy Cover under Fertilizer Stress (%)	Degree of Canopy Decay	Reduced Maximum Canopy Cover (%)	Decrease in Canopy Growth Coefficient (%)	Average Canopy Reduction (%)	Standardized Crop Water Productivity Reduction (%)
N1 (120 kg/ha)	71	81.7	Small	14	4	0.40	34
N2 (220 kg/ha)	82	90.2	Small	5	3	0.28	28
N3 (320 kg/ha)	75	84.5	Small	11	3	0.30	34

. The calibrated fertilizer stress coefficients are tabulated in Table 2.

3.2. Creation of the AquaCrop Modeling Database

3.2.1. Meteorological Data

The meteorological data, encompassing minimum/maximum air temperatures (°C), daily precipitation (mm), and wind velocity (m/s) within the experimental area, were acquired from a high-precision automatic meteorological station (HM-HL08). Evapotranspiration values, derived from the ET0 calculator integrated within the AquaCrop version 6.1 software, were used as a reference. This dataset facilitated the constitution of a meteorological database within the software. Daily weather data spanning two years are shown in Figure 2 and Figure 3.

3.2.2. Crop Data

The crop parameters were obtained during the growth and development of winter wheat within the experimental area. They were then input into the crop module of the AquaCrop model to formulate a crop database. This database includes information such as initial canopy cover, planting density, canopy cover across the entire lifecycle, and key crop developmental phases including attainment of maximum canopy cover, flowering, and the timing of maturity and senescence. The AquaCrop model offers two modes to depict crop growth and development: calendar mode and growing degree-day (GDD) mode. To accommodate varying climatic conditions across different years and to provide a more precise depiction of crop growth, the GDD mode was employed for inputting crop data.

Subsequently, following the research approach of Xing et al. [37] which entailed a sensitivity analysis of winter wheat parameters based on the extended Fourier amplitude sensitivity test (EFAST) method, this study utilized the growth data of winter wheat from the experimental area for the years 2021 to 2022 to adjust and calibrate the model parameters. The “trial and error method” was employed to debug the model parameters, aligning them within the parameter ranges provided in the model operation manual. Some of the calibrated model crop parameters are presented in

Table 3. Selected calibrated parameters of the Aquacrop model.

Model Parameter	Notation	Calibrated Value	Default Parameter Values	Unit
Reference harvest index	HI0	48	45–50	%
Base temperature	Tbase	0	0	°C
Upper temperature	Tupper	26	26	°C
Canopy growth coefficient	CGC	3.60	1–5	%/d
Canopy attenuation coefficient	CDC	0.313	0.1–0.5	%/d
Maximum effective root depth	ZX	1	0.8–1.5	m
Standardized water productivity	WP*	17	11–22	g/m3
Sowing to seedling emergence time	/	277	150–280	GDD
Seeding to maximum canopy cover time	/	1734	Time to emergence +1000–2000	GDD
Sowing to senescence time	/	1815	Time to emergence +1000–2000	GDD
Sowing to ripening time	/	2425	Time to emergence +1500–2900	GDD
Upper threshold for the effect of water stress on canopy growth	Pexp,upper	0.20	0.14–0.26	/
Lower threshold for the effect of water stress on canopy growth	Pexp,lower	0.55	0.45–0.84	/
Upper threshold for the effect of water stress on stomatal closure	Psto,upper	0.65	0.60–0.67	/
Upper threshold for the effect of water stress on canopy senescence	Psen,upper	0.70	1.75–3.25	/

. The model parameters were then validated using the growth data of winter wheat from the experimental area for the years 2022 to 2023.

3.2.3. Field Management Data and Soil Parameter Data

The crop management practices in the experimental area were conducted in accordance with the local winter wheat field management guidelines, with a particular emphasis on pest and weed control. The respective field management parameters and their values were compiled into a database. Soil parameters, including soil depth, soil particle size and mass fraction corresponding to each soil depth, and physical properties such as field water holding capacity, saturated water content, and permanent wilting point, were incorporated into the AquaCrop model to establish a soil parameter database. The details pertaining to these soil parameters are presented in

Table 4. Physical properties of soil at 0–100 mm depth in the experimental area.

Soil Depth (mm)	Soil Particle Size Mass Fraction (%)			Physical Parameter
	Sand	Silt	Clay	Permanent Wilting Point (%)	Field Water Holding Capacity (%)	Saturated Water Content (%)
0–20	0.17	0.64	0.19	20.4	33.3	36.5
20–40	0.11	0.65	0.24	20.9	35.5	38
40–60	0.09	0.65	0.26	19.7	35.4	40
60–80	0.08	0.65	0.27	21.1	35.6	38
80–100	0.05	0.61	0.34	21.4	35.7	38

.

3.3. Testing Methods for Evaluating AquaCrop Model Accuracy

The AquaCrop model is capable of simulating variations in canopy cover, aboveground biomass, yield, and soil water content throughout the crop reproductive period. Upon the establishment of the crop, meteorological and soil databases within the model, the calibration of model crop parameters, and the growth data of winter wheat from the experimental area for the period 2022 to 2023 was compared against the data generated from the model run. The following indices were employed to assess the accuracy of model calibration and verification in this study: the coefficient of determination (R²), normalized root mean square error (NRMSE), and consistency index (d).

The simulation effect is considered better as the values of d and R² approach 1, with the optimal value being 1. An NRMSE value below 10% indicates excellent model simulation; a value between 10% and 20% indicates good simulation; a value between 20% and 30% suggests the simulation is generally effective; and a value greater than 30% denotes poor simulation. The model evaluation indices are computed using the formulas:

$$R^2=\frac{{\left[{\displaystyle {\sum }_{i=1}^n\left(S_i-\overline{S}\right)\left(O_i-\overline{O}\right)}\right]}^2}{{\displaystyle {\sum }_{i=1}^n{\left(S_i-\overline{S}\right)}^2{\displaystyle {\sum }_{i=1}^n{\left(O_i-\overline{O}\right)}^2}}}$$

(9)

$$NRMSE=\sqrt{\frac{1}{n}{{\displaystyle {\sum }_{i=1}^n\left(S_i-O_i\right)}}^2}\times 100/\overline{O}$$

(10)

$$d=1-\frac{{\displaystyle {\sum }_{i=1}^n{\left(S_i-O_i\right)}^2}}{{\displaystyle {\sum }_{i=1}^n{\left(\left|S_i-\overline{O}\right|+\left|O_i-\overline{O}\right|\right)}^2}}$$

(11)

where n is the number of measured values; $S_i$ is the analog value; $O_i$ is the measured value; $\overline{S}$ is the mean of the analog values; $\overline{O}$ is the mean of the measured values.

3.4. Calibration and Validation of the Model and Crop Data Calibration

3.4.1. Calibration and Validation of Canopy Cover and Aboveground Biomass

Following the sequential calibration approach by Vanuytrecht et al. [38], this paper first calibrated the canopy cover, followed by aboveground biomass, and finally the crop yield. Measurements from 2021 to 2022 were used to calibrate the model, measurements from 2022 to 2023 were used to validate the model, and the growth data of winter wheat in the experimental area from 2022 to 2023 were employed for validating the model parameters. Figure 4 and Figure 5, along with

Table 5. Indices of model calibration and validation accuracy.

Model Calibration and Validation	Water and Fertilizer Treatment	Canopy Cover (%)			Aboveground Biomass (t/ha)			Soil Moisture Content (%)
		R2	NRMSE	d	R2	NRMSE	d	R2	NRMSE	d
Calibration	W1N1	0.92	15.5	0.91	0.96	8.6	0.96	0.92	2.4	0.96
	W1N2	0.98	7.9	0.97	0.96	7.7	0.96	0.96	4.9	0.90
	W1N3	0.92	15.3	0.91	0.98	3.4	0.97	0.88	2.9	0.94
	W2N1	0.96	9.4	0.96	0.96	4.6	0.98	0.72	3.7	0.90
	W2N2	0.98	7.2	0.96	0.98	6	0.96	0.94	3.9	0.92
	W2N3	0.98	10.7	0.96	0.98	4.4	0.98	0.97	3.6	0.90
	W3N1	0.97	11.7	0.94	0.96	3.7	0.99	0.96	2.9	0.95
	W3N2	0.98	11.4	0.95	0.98	4.2	0.97	0.96	3.9	0.91
	W3N3	0.98	11.9	0.94	0.97	3.2	0.98	0.94	3.4	0.94
Validation	W1N1	0.92	11.7	0.90	0.99	3.9	0.98	0.98	6.6	0.92
	W1N2	0.94	10.4	0.92	0.99	3.4	0.98	0.95	5.7	0.93
	W1N3	0.94	8.5	0.93	0.99	4.6	0.97	0.97	5.1	0.96
	W2N1	0.96	8.7	0.93	0.98	4.1	0.98	0.97	3	0.94
	W2N2	0.98	6.3	0.96	0.98	5.1	0.97	0.98	2.7	0.91
	W2N3	0.98	6.1	0.96	0.98	4.6	0.91	0.99	2	0.95
	W3N1	0.98	7.5	0.94	0.99	2.8	0.99	0.98	3.2	0.94
	W3N2	0.98	5.1	0.97	0.98	6.5	0.95	0.98	4.1	0.91
	W3N3	0.98	7	0.95	0.99	3.7	0.98	0.99	3.1	0.95

, illustrate the results of both processes. During calibration, for each water and fertilizer treatment of winter wheat, the coefficient of determination, R², ranged between 0.92 to 0.98 for canopy cover and 0.96 to 0.98 for aboveground biomass. The NRMSE varied from 7.2 to 15.5 for canopy cover and 3.2 to 8.6 for aboveground biomass, while the consistency index, d, ranged from 0.91 to 0.96 for canopy cover and 0.96 to 0.99 for aboveground biomass.

The growth data from the experimental area for the period 2022 to 2023 was used for model validation. For each water-fertilized treatment of winter wheat, the R² values ranged from 0.92 to 0.98 for canopy cover and 0.98 to 0.99 for aboveground biomass. The NRMSE values varied between 5.1 to 11.7 for canopy cover and 2.8 to 6.5 for aboveground biomass, while the d values ranged from 0.90 to 0.97 for canopy cover and 0.91 to 0.99 for aboveground biomass. The above results showed that the Aquacrop model can simulate the canopy cover, biomass, and yield of winter wheat under different irrigation and fertilization regimes better where the coefficient of determination R², the standard root mean square error NRMSE, and the consistency index d between the simulated and measured values were within acceptable limits. See Figure 6, Figure 7 and Figure 8 for specific comparison charts.

3.4.2. Calibration of Yield, WUE, and PFP

WUE serves as an indicator of water absorption and utilization by winter wheat, while fertilizer PFP serves as a comprehensive index to assess fertilizer application and the local soil base nutrient situation. The accuracy of the model simulation for yield, WUE, and PFP data of winter wheat is demonstrated through comparisons of measured and simulated values, as shown in

Table 6. Accuracy test indices for water and fertilizer indicators.

Year	Treatment	Yield (kg/ha)		R2	NRMSE	d	WUE (kg/m3)		R2	NRMSE	d	PFP (kg/kg)		R2	NRMSE	d
		Measured	Analog				Measured	Analog				Measured	Analog
2021–2022	W1N1	6168	6012	0.99	1.78	0.98	13.27	12.99	0.95	1.78	0.98	25.70	25.05	0.99	1.61	0.99
	W1N2	6586	6566				13.90	13.97				27.44	27.36
	W1N3	6371	6343				13.16	13.37				26.55	26.43
	W2N1	7699	7605				14.03	14.43				17.50	17.28
	W2N2	8138	8053				14.93	15.35				18.50	18.30
	W2N3	7900	7680				14.27	14.36				17.96	17.45
	W3N1	7538	7477				12.14	12.11				11.78	11.68
	W3N2	7842	7730				12.34	12.16				12.25	12.08
	W3N3	7670	7633				12.51	12.61				11.98	11.93
2022–2023	W1N1	5002	5030	0.99	0.64	0.99	9.54	9.52	0.99	0.75	0.99	41.92	41.69	0.99	0.61	0.99
	W1N2	5912	5902				10.69	10.66				49.18	49.27
	W1N3	5573	5543				10.06	10.03				46.19	46.45
	W2N1	6330	6303				10.37	10.28				28.65	28.78
	W2N2	7094	7003				11.46	11.39				31.83	32.25
	W2N3	6650	6624				10.88	10.78				30.11	30.23
	W3N1	5981	5999				9.21	9.33				18.75	18.69
	W3N2	6545	6591				10.11	10.06				20.60	20.46
	W3N3	6232	6224.				9.81	9.69				19.45	19.48

.

For each treatment over two years, the R² values for yield were 0.99 and 0.99; NRMSE values were 1.78 and 0.64; and d values were 0.98 and 0.99, respectively. Similarly, for WUE, the R² values were 0.95 and 0.96; NRMSE values were 1.78 and 2.63; and d values were 0.98 and 0.98, respectively. For PFP, the R² values were 0.99 and 0.99; NRMSE values were 1.60 and 0.62; and d values were 0.99 and 0.99, respectively.

These statistical values underscore the high accuracy achieved in the calibration of yield, WUE, and PFP data for winter wheat. Thus, the AquaCrop model proves a viable tool for simulating various irrigation and fertilization scenarios for winter wheat to determine optimal irrigation and fertilization systems, aiming to enhance yield while conserving water and fertilizer resources.

4. Discussion

4.1. Simulation Scenarios

Overwintering irrigation refers to irrigation before winter to stabilize the ground temperature, increase soil moisture, and enable winter wheat to overwinter safely. The growth trajectory of winter wheat is significantly influenced by moisture levels, especially during the period extending from the jointing to the filling stage [39]. To further understand the impact of irrigation on the yield and other indices of winter wheat across different fertility phases, a multi-scenario simulation was conducted. Firstly, we calibrated the model parameters based on two years of field experimental data, and then explored the optimal irrigation and nitrogen application scheme based on this model.

In the scenario design, this study used the 2022–2023 meteorological data as the base data, uniformly setting the crop sowing date as October 15, determined the start of the overwintering period W as 15 December, the start of the greening period G as 15 March, the start of the nodulation period J as 15 April, and the start of the filling period F as 15 May. Three nitrogen application levels were selected: N1 (120 kg/ha), N2 (220 kg/ha), and N3 (320 kg/ha), along with three irrigation levels: W1 (60%θ_f), W2 (70%θ_f), and W3 (80%θ_f) (where θ_f is the field water holding capacity). Then, altering a single irrigation event for the growth period with an irrigation volume of 45 mm, resulted in a total of 36 irrigation and nitrogen application combination schemes, as shown in

Table 7. Simulation scenarios for nitrogen application by flooding.

Program Number	Water and Fertilizer Treatment	Flooding Time	Irrigation Quota (mm)	Nitrogen Application (kg/hm2)	Program Number	Water and Fertilizer Treatment	Flooding Time	Irrigation Quota (mm)	Nitrogen Application (kg/hm2)
T1	W1N1	W	180	120	T19	W2N2	J	270	220
T2	W1N1	G	180	120	T20	W2N2	F	270	220
T3	W1N1	J	180	120	T21	W2N3	W	270	320
T4	W1N1	F	180	120	T22	W2N3	G	270	320
T5	W1N2	W	180	220	T23	W2N3	J	270	320
T6	W1N2	G	180	220	T24	W2N3	F	270	320
T7	W1N2	J	180	220	T25	W3N1	W	405	120
T8	W1N2	F	180	220	T26	W3N1	G	405	120
T9	W1N3	W	180	320	T27	W3N1	J	405	120
T10	W1N3	G	180	320	T28	W3N1	F	405	120
T11	W1N3	J	180	320	T29	W3N2	W	405	220
T12	W1N3	F	180	320	T30	W3N2	G	405	220
T13	W2N1	W	270	120	T31	W3N2	J	405	220
T14	W2N1	G	270	120	T32	W3N2	F	405	220
T15	W2N1	J	270	120	T33	W3N3	W	405	320
T16	W2N1	F	270	120	T34	W3N3	G	405	320
T17	W2N2	W	270	220	T35	W3N3	J	405	320
T18	W2N2	G	270	220	T36	W3N3	F	405	320

.

4.2. Scenario Analysis Results and Determination of Optimal Water and Fertilizer Management System

4.2.1. Scenario Analysis Results

Table 8. Simulated values of winter wheat yield, WUE, and PFP under scenario analysis.

Program Number	Yield (kg/hm2)	WUE (kg/m3)	PFP (kg/kg)	Program Number	Yield (kg/hm2)	WUE (kg/m3)	PFP (kg/kg)
T1	5025	10.77	41.88	T19	6996	14.13	31.80
T2	5045	10.89	42.04	T20	6991	14.11	31.78
T3	5043	10.87	42.03	T21	6528	13.17	20.40
T4	5028	10.80	41.90	T22	6614	13.38	20.67
T5	5838	11.92	26.54	T23	6611	13.37	20.66
T6	5906	12.08	26.85	T24	6582	13.30	20.57
T7	5901	12.07	26.82	T25	5796	10.15	48.31
T8	5868	12.00	26.67	T26	5804	10.21	48.37
T9	5514	11.29	17.23	T27	5799	10.20	48.33
T10	5542	11.36	17.32	T28	5798	10.17	48.32
T11	5539	11.36	17.31	T29	6584	11.33	29.93
T12	5528	11.33	17.28	T30	6590	11.36	29.96
T13	6034	12.09	50.28	T31	6589	11.36	29.95
T14	6067	12.30	50.56	T32	6588	11.35	29.95
T15	6066	12.26	50.55	T33	6221	10.94	19.44
T16	6054	12.19	50.45	T34	6223	10.97	19.45
T17	6985	14.07	31.75	T35	6223	10.97	19.45
T18	6998	14.15	31.81	T36	6222	10.95	19.44

shows that, with Programs T1–T12 for instance, under the same irrigation level, the crop yield initially increased and then decreased with the rise in nitrogen application. Similarly, under a constant nitrogen application level, the crop yield initially increased and then decreased with the increase in irrigation volume.

Under identical irrigation and fertilization conditions, irrigation at varied fertility stages also resulted in certain yield differences. For instance, with Programs T1–T4, the corresponding yields were 5025, 5045, 5043, and 5028 kg/ha, respectively, indicating higher yields during the jointing or re-greening stages compared to the overwintering or filling stages. This highlights the influence of irrigation timing on yield.

Moreover, contrasting Programs T17–T20 with T29–T32 reveals that with sufficient irrigation, increasing irrigation volume diminishes the yield variance caused by irrigation at different fertility stages, without enhancing yield, but reducing WUE instead.

4.2.2. Impact of Water–Fertilizer Coupling on Yield, WUE, and PFP

The investigation of water–fertilizer coupling effects on yield, WUE, and PFP was carried out by selecting simulated scenarios yielding optimal results under the same water–fertilizer treatments, with significance analyses performed using IBM SPSS.

Significant differences (p < 0.05) in yield, WUE, and PFP of winter wheat under the same and different fertilizer treatments are shown in

Table 9. Effect of water–fertilizer coupling on yield, WUE, and PFP.

Program Number	Flooding Treatment	Fertilizer Treatment	Yield (kg/hm2)	WUE (kg/m3)	PFP (kg/kg)
T2	W1	N1	5035 ± 10 cC	10.83 ± 0.057 cB	41.96 ± 0.086 aC
T6	W1	N2	5878 ± 31 aC	12.02 ± 0.074 aB	26.72 ± 0.144 bC
T10	W1	N3	5530 ± 12 bC	11.34 ± 0.033 bB	17.28 ± 0.04 cC
T14	W2	N1	6055 ± 15 cA	12.21 ± 0.092 cA	50.46 ± 0.128 aA
T18	W2	N2	6992 ± 5 aA	14.12 ± 0.034 aA	31.79 ± 0.027 bA
T22	W2	N3	6584 ± 39 bA	13.31 ± 0.097 bA	20.58 ± 0.125 cA
T26	W3	N1	5799 ± 3 cB	10.18 ± 0.028 cC	48.33 ± 0.027 aB
T30	W3	N2	6588 ± 2 aB	11.35 ± 0.014 aC	29.95 ± 0.012 bB
T34	W3	N3	6222 ± 1 bB	10.96 ± 0.015 bC	19.44 ± 0.005 cB
Flooding treatment			**	**	*
Fertilizer treatment			**	**	**
Flooding treatment × Fertilizer treatment			**	**	*

Note: Different lowercase letters indicate significant differences (p < 0.05) in winter wheat parameters at varying fertilization treatment levels within the same irrigation treatment level; different uppercase letters indicate significant differences (p < 0.05) in winter wheat parameters at varying irrigation treatment levels within the same fertilization treatment level. Symbols * and ** denote significance levels (p < 0.05) and (p < 0.01), respectively.

and Figure 7. Both yield and WUE showed a tendency to increase and then decrease under the same irrigation conditions or the same fertilization conditions. Furthermore, Table 9 reveals the highly significant effects (p < 0.01) of irrigation and fertilization treatments on winter wheat yield and WUE, while irrigation treatment significantly affected PFP (p < 0.05). The interaction between irrigation and fertilization treatments also displayed significant effects on yield, WUE, and PFP of winter wheat (p < 0.05).

4.2.3. Determination of Optimal Water and Fertilizer Management System Based on Yield and WUE

To analyze the overall trend of irrigation and fertilization effects on yield, WUE, and PFP, a synthesis of scenario analysis results was performed, followed by regression analyses. Yield, WUE, and PFP were treated as dependent variables, while irrigation and fertilization served as independent variables. Regression models were established and expressed using binary quadratic regression equations, as presented in Equation (12).

$$z=a_0+a_1\times x+a_2\times y+a_{12}\times x\times y+a_{11}\times x^2+a_{22}\times y^2$$

(12)

where z represents yield, WUE, and PFP, respectively; x and y are dimensionless variables; a₀ is the constant term; a₁ and a₂ are the coefficients of the primary term; a₁₂ is the coefficient of the interaction term; and a₁₂ and a₁₂ are the coefficients of the quadratic term [33].

Utilizing Origin 2021, response surface relationship plots concerning irrigation, fertilization, and yield, WUE, and PFP were drawn and analyzed, with the outcomes displayed in Figure 8. Examination of

Table 10. Regression relationship between water and fertilizer supply and yield, WUE, and PFP.

Dependent Variable z	Regression Equation	R2	Combination When Z Is the Maximum Value
			X (mm)	Y (kg/hm2)	Zmax
Yield (kg/ha)	Z = −2917.942 + 41.090x + 30.087y − 0.00196xy − 0.06412x2 − 0.06156y2	0.9959	317.900	242.580	7189.340
WUE (kg/m3)	Z = −5.267 + 0.096x + 0.047y + 5.100 × 10−6xy − 1.705 × 10−4x2 − 1.012 × 10−4y2	0.9858	281.610	236.120	14.022
PFP (kg/kg)	Z = 41.392 + 0.213x − 0.271y − 8.303× 10−5xy − 3.349 × 10−4x2 + 3.530 × 10−4y2	0.9904	332.000	120.000	50.547

Note: x represents the amount of irrigation water, and y represents the amount of fertilizer applied.

and Figure 8 reveals that winter wheat yield is influenced by both water and fertilizer factors, which either promote or inhibit each other. The two-dimensional projection of the response surface in Figure 6 vividly shows that, at certain irrigation or fertilizer levels, the yield of winter wheat follows a pattern of initial increase followed by a decline. The regression equation shows that the regression coefficients for irrigation volume and fertilizer application volume were positive (41 and 30 respectively), indicating that within a certain range, both factors contribute to an increase in yield, although the impact of irrigation volume (x) is more significant than that of fertilizer application (y). At the point of maximum yield (7189 kg/ha), the irrigation volume was 317 mm, and the fertilizer application amount was 242 kg/ha, aligning with the findings from treatments T17–T20.

The varying irrigation and fertilization treatments had notable effects on both the WUE and PFP of winter wheat. Increasing the irrigation amount or fertilizer application initially led to an increase in WUE, which peaked at 14.022 kg/m³ (when irrigation was 281.61 mm and fertilizer was 236.12 kg/ha, comparable to treatments T17–T20), before declining. Similarly, an increment in irrigation volume initially led to an increase in PFP, which then descended, while an increase in fertilizer application rate caused a consistent decrease in PFP. Merely pursuing the maximum PFP would significantly diminish both yield and WUE, which contradicts the practical goal of achieving high yield alongside water conservation. Hence, the confidence interval at which both yield and WUE attain their optimum was taken into account.

Based on calculations, a yield exceeding 99% of the maximum value can be achieved when the irrigation volume ranges from 296 to 339 mm and the fertilizer application rate is between 229 to 261 kg/ha. Concurrently, a WUE nearing 99% of the maximum value is attainable with an irrigation volume of between 267 to 303 mm and a fertilizer application rate ranging from 210 to 268 kg/ha. Considering the objectives of high yield, water, and fertilizer conservation, an optimal interval was selected with an irrigation volume of 296 to 303 mm and a fertilizer application rate of 229 to 261 kg/ha. During this interval, the PFP ranged from 27 to 31 kg/kg, which was about 60% of the maximum PFP value, aligning more with the actual scenario. This interval closely corresponded with the outcomes of the W₂N₂ treatment in the two-year field experiment, suggesting that the regression equation, based on scenario design results, fitted well. This interval can thus offer a reference for the irrigation and fertilization system of winter wheat in the irrigation area of the Yellow River Basin.

5. Discussion

5.1. Model Calibration and Validation

In this study, the AquaCrop model was calibrated and validated using measured values of canopy cover, yield, above-ground biomass, and soil moisture content from two years of field experiments. Following validation, this model was employed to simulate the changing patterns of yield, WUE, and PFP of winter wheat under various irrigation schemes across different fertility periods. Scenario simulations were conducted to optimize water and nitrogen regimes. The results demonstrated that the AquaCrop model could accurately simulate the canopy cover and aboveground biomass of winter wheat under different irrigation and fertilization treatments. The R², NRMSE, and d were all found to be within an acceptable range. Specifically, the ranges of R², NRMSE, and d for canopy cover across various winter wheat treatments were 0.92–0.98, 7.2–15.5, and 0.91–0.96, respectively. For aboveground biomass, these ranges were 0.96–0.98, 3.2–8.6, and 0.96–0.99, respectively. These findings align with the study of Teng et al. [39], which also reported high accuracy in predicting canopy cover and aboveground biomass of winter wheat.

Additionally, for all treatments, the R² and NRMSE values for winter wheat yield were 0.99 and 1.78, respectively; for WUE, they were 0.95 and 1.78, respectively. It was observed that during the calibration stage, the measured values of winter wheat yield were greater than the simulated values. However, during the validation stage, some simulated values of winter wheat yields were higher than the measured values in treatments after increasing water and fertilizer, which aligned with the findings of Guo et al. [40]. This discrepancy might be due to the increased model error when soil moisture or fertilizer stress appeared as a result of raising water and fertilizer application in the treatment.

Regarding the canopy cover of winter wheat, the simulated value of canopy cover before the overwintering period was larger compared to the measured value, similar to the results of the applicability evaluation of winter wheat by Chen et al. [30] This discrepancy could be associated with the fact that in reality, winter wheat almost halted growth during the overwintering period, keeping the canopy cover nearly unchanged, whereas the model continued to indicate an increase in canopy cover. During the crop’s aboveground biomass accumulation process, the simulated values of the model and the measured values followed a nearly similar trend. However, the model’s simulation of aboveground biomass during the reproductive period was higher than the measured values overall. This was unlike the results of Andarzian et al. [12], where the model simulated aboveground biomass lower than the measured values at the late reproductive stage. This discrepancy might be tied to the fact that the distribution of irrigation dates in the present experiments was more evenly spread out, leading to minor changes in soil moisture stress, as opposed to the experiments of Andarzian et al. [12], where water stress in the soil decreased with the reduction of nitrogen application in late irrigation. The model might not have adequately considered the water and nitrogen stress in the soil. Nonetheless, overall, the model simulation was satisfactory, and the calibrated model can be employed for local winter wheat yield prediction.

5.2. Scenario Simulation and Treatment Analysis

The scenario simulation in this paper using the calibrated model illustrated that under different irrigation and fertilization conditions, the T17–T20 scenarios exhibited the highest yield and WUE, aligning with the experimental results from the two-year field experiment, which showcased the highest yield and WUE under the W₂N₂ treatment. This study also deduced that under identical irrigation and fertilization conditions, the crop yield would be larger when irrigated at the jointing or re-greening stage as opposed to the overwintering or filling stage. Li et al. [34] demonstrated that irrigation at the jointing stage could significantly enhance leaf WUE and seed yield of winter wheat, with the yield increase attributed to a notable rise in the number of spikes. Similarly, Han et al. [41] found that irrigation at the jointing stage was more conducive to improving WUE and dry matter accumulation in winter wheat, thereby boosting the yield of winter wheat. This aligns well with the simulation results of irrigation at different fertility stages under the same irrigation and fertilization conditions. Concurrently, under the same irrigation conditions, winter wheat yield exhibited a trend of increasing and then decreasing with the rise in fertilizer application. Under identical fertilization conditions, a similar trend was observed with increasing irrigation, which is in line with the experimental results of Jia et al. [42], that under the same amount of irrigation, the dry matter accumulation of wheat increased with the rise in nitrogen application.

5.3. Water–Fertilizer Coupling Effects and Optimal Regimes

In the process of exploring the impacts of water–fertilizer coupling on yield, WUE, and PFP, it was found that both irrigation and fertilization treatments, along with the interaction between these two factors, exhibited highly significant effects (p < 0.01) on the yield and WUE of winter wheat. Additionally, the irrigation treatment and the interaction between the two factors demonstrated significant effects (p < 0.05) on the PFP of winter wheat. These findings were consistent with the study by Albrizio et al. [43] who showed that both water and nitrogen application were pivotal factors influencing the growth of winter wheat, and that appropriate irrigation coupled with increased nitrogen application can increase the yield of winter wheat.

In this paper, the employment of fitted coupled water–fertilizer regression equations facilitated the construction of response surface plots, which were helpful in identifying optimal irrigation and fertilization intervals. It was concluded that excessive irrigation could significantly reduce WUE, whereas an appropriate amount of irrigation could enhance the water adoption efficiency of the crop. This claim aligns with the findings of Chen et al. [44], who suggested that excessive soil water could impair nutrient uptake of the crop due to its impact on the respiration of crop roots. They further suggested that appropriate water stress could be more beneficial to crop growth and is more conducive to WUE.

In this investigation, it was identified that within the irrigation amount range of 296.13 to 303.39 mm, and the fertilizer application rate range of 229.67 to 261.94 kg/ha, the yield and WUE could attain more than 99% of the maximum value. These results aligned with the data acquired from two years of field experiments, thereby providing a valuable reference for the determination of irrigation and fertilizer application amounts in the irrigation area of the Yellow River Basin. Furthermore, these findings can be employed as a reference for fertilizer application strategies within the irrigation area of the Yellow River Basin, thereby contributing to the broader objective of optimized agricultural water management in this region.

6. Conclusions

Based on the extensive use of the Aquacrop model globally and the more accurate simulation results of the model in different regions of the world, it can be seen that the Aquacrop model has strong applicability to different regions and crops, and attention should be paid to the accuracy of the data inputted into the model, including climatic data, crop data, field management data, etc., when using the model.

The Aquacrop model has proven to be effective at simulating the canopy cover, yield, and aboveground biomass among other parameters of winter wheat in the irrigation area of the Yellow River Basin. The model calibration assessment indices have all satisfied the requisite criteria, demonstrating its reliability. Moreover, utilizing the calibrated localized model to predict the yield of winter wheat, when irrigated at varying fertility periods, aligns well with the outcomes of the two-year field trials. The simulation reveals that both yield and WUE follow a pattern of initial increase, followed by a decrease, with the escalation of irrigation volume and fertilizer application.

Furthermore, through response surface regression analysis, it was deduced that to attain 99% of the maximum value for yield and WUE, the irrigation volume should range between 296.13 mm and 303.39 mm, while the fertilizer application rate should be within the span of 229.67 kg/ha to 261.94 kg/ha. These findings are in line with the results from the field trials and serve as valuable reference points for determining the irrigation and fertilizer application rates for winter wheat in the irrigation area of the Yellow River Basin. Such insights not only confirm the findings of the field experiment but also extend a practical framework for optimized agricultural water management in this particular region.