Experimental site.

Field experiments were carried out at the agricultural research station in Zhuji, Zhejiang Province, China, spanning the 2021 to 2023 growing seasons. Zhuji lies within a subtropical monsoon climate zone. The area receives an average annual precipitation of 1500 mm and maintains an average temperature of 16 °C. Monthly temperatures vary from 4 °C in January to 28 °C in July. The area receives ∼2000 h of sunshine annually. Experimental plots were established on loamy soil characterized by well-defined layers. The topsoil, extending 0 to 20 cm deep, is rich in organic matter and exhibits a bulk density of 1.25 g·cm⁻³, containing 120 mg·kg⁻¹ nitrogen, 30 mg·kg⁻¹ phosphorus, and 200 mg·kg⁻¹ potassium, with 3.5% organic matter content. The subsoil layer, 20 to 40 cm deep, features a bulk density of 1.35 g·cm⁻³ and comprises 80 mg·kg⁻¹ nitrogen, 20 mg·kg⁻¹ phosphorus, 150 mg·kg⁻¹ potassium, and 2.0% organic matter. In the deeper layer, 40 to 60 cm beneath the surface, the soil has a bulk density of 1.40 g·cm⁻³ and contains 60 mg·kg⁻¹ nitrogen, 15 mg·kg⁻¹ phosphorus, and 100 mg·kg⁻¹ potassium, with an organic matter percentage of 1.5%.

Over 3 years, the average minimum temperature rose each month from February to May (Fig. 1). Precipitation levels varied annually over the 3-year period. In 2021, March saw the highest precipitation, at 225.3 mm, with lower levels in other months. Although adequate March precipitation aids cabbage growth by providing necessary moisture, excessive rainfall can waterlog soils, adversely affecting root respiration and nutrient uptake. In 2022, February experienced higher precipitation at 130.0 mm, with lower amounts following in subsequent months. This pattern provides sufficient water in early spring but may necessitate supplementary irrigation during peak growth periods, such as May, to ensure optimal moisture availability. The 2023 precipitation was more evenly distributed, peaking in May with 158.2 mm. Consistent rainfall throughout the growing season supports steady water availability, reducing drought stress risks on cabbage.

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Experimental design.

Over 2 years, the study evaluated eight different fertilization regimes for cabbage (Brassica oleracea var. capitata). Treatments were divided into high (21HF, 22HF, 23HF), medium (22MF, 23MF), and low (22LF, 23LF) fertilization levels, and severe nitrogen stress (230F). All treatments used the ‘Jinqiu’ variety of cabbage. Each treatment varied in the application of nitrogen (N), phosphorus (P₂O₅), and potassium (K₂O), along with the number of fertilization events. Table 1 presents detailed information about the treatments, including seeding, transplanting, and harvest dates.

Table 1. Fertilization treatments and key dates for cabbage cultivation from 2021 to 2023.

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This study assessed cabbage growth and nutritional quality across various fertilization treatments. Key indicators, including head yield, protein content, leaf number, nitrogen content, leaf area index, tops weight, and harvest index, were measured and are detailed in Table 2. These measurements aimed to evaluate how different fertilization rates and frequencies affect cabbage growth and quality.

Table 2. Comprehensive measurement parameters for cabbage growth assessment.

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Model description.

CROPGRO, a process-oriented model, simulates daily plant growth by integrating the dynamics of crop carbon, soil water, and soil nitrogen. The model necessitates daily weather data—including temperatures, precipitation, and solar radiation—and soil physical and chemical properties, along with crop management details and genotype information. The model produces daily predictions of plant dry matter, leaf area index, canopy development, and movements of soil water and salts, while also assessing water and nitrogen stress and tracking phenological stages. Within the model, the cabbage head is depicted as a “pod,” with its development classified as a generative organ. In CROPGRO, the stem is categorized as a vegetative organ for both cabbage and Chinese cabbage, even though it is part of the economically important tissue of the head. Only the cabbage head’s leaves are considered part of the pod. The model calculates the net pod growth rate as the sum of the shell and seed growth rates.$$\text{WPDOT}=\text{WSHDOT}+\text{WSDDOT},$$ [1] where WSHDOT is Net shell growth rate (g⋅m⁻²⋅d⁻¹ shell)(g⋅m⁻²⋅d⁻¹ shell); WSDDOT is Net seed growth rate (g⋅m⁻²⋅d⁻¹ shell) (g⋅m⁻²⋅d⁻¹ shell).$$\mathit{WSHDOT}=\mathit{WSHDTN}-\mathit{WSHIDT}-\mathit{WTABRT}-\mathit{NRUSSH}/0.16-\mathit{CRUSSH}$$ [2] where WSHDTN is the new shell growth today (g·m⁻²·d⁻¹ shell)(g·m⁻²·d⁻¹ shell), representing the daily increase in shell mass due to growth; WSHIDT is the weight of shell tissue consumed by pests today (g·m⁻²·d⁻¹ shell)(g·m⁻²·d⁻¹ shell), indicating the reduction in shell mass due to pest activity; WTABRT is the weight of shells aborted on a day (g·m⁻²·d⁻¹ shell)(g·m⁻²·d⁻¹ shell), accounting for the shell mass lost due to abortion; NRUSSH is the nitrogen actually mobilized from shells in a day (g·m⁻²·d⁻¹ N) (g·m⁻²·d⁻¹ N), representing the amount of nitrogen relocated from the shell to other parts of the plant; and CRUSSH is the carbon mobilized from shell tissue in a day (g·m⁻²·d⁻¹ CH₂O).$$\mathit{WSDDOT}=\mathit{WSDDTN}-\mathit{SWIDOT}$$ [3] where WSDDTN is the new seed growth today (g·m⁻²·d⁻¹ seed)(g·m⁻²·d⁻¹ seed), representing the daily increase in seed mass due to growth; and SWIDOT is the daily seed mass damage (g·m⁻²·d⁻¹)(g·m⁻²·d⁻¹), indicating the reduction in seed mass due to various damaging factors.

Model evaluation.

In 2022 and 2023, models were evaluated by comparing observed and simulated data for variables such as leaf area index (LAI), leaf number, tops weight, head yield, and head protein content. Fertilization treatments varied for spring cabbage in Zhuji, Zhejiang Province, to validate model predictions across different nutrient management scenarios. Model accuracy was assessed using three indicators: deviation ratio (d), relative root mean square error (RRMSE), and a comparison of observed vs. simulated values. A lower deviation ratio indicates higher accuracy of simulated results. RRMSE, a unit-independent measure of homogenization error, indicates accuracy; smaller values signify minor differences between observed and simulated data. The evaluation criteria for RRMSE are 0 to 0.1 (excellent), 0.1 to 0.2 (good), 0.2 to 0.3 (fair), and >0.3 (poor).$$d=\frac{s_i-o_i}{o_i}\times 100\text{\%}$$ [4] $$\mathit{RRMSE}=\frac{\sqrt{{{\displaystyle \sum }}_{i=1}^n\frac{{(s_i-o_i)}^2}{n}}}{{{\displaystyle \sum }}_{i=1}^n\frac{o_i}{n}}\times 100\text{\%}$$ [5] where s_i is the simulated value, o_i is the observed value, and n is the sample size.

Optimization principle of fertilization management.

This study designed fertilization treatments to explore the effects of varying nitrogen (N), phosphorus (P), and potassium (K) application rates and schedules on cabbage growth using the CROPGRO model. Nitrogen fertilization was applied in a range from 0 to 400 kg·hm⁻² in 10-kg increments. The N:P₂O₅:K₂O ratio was consistently maintained at 2:1:2. Fertilization frequency ranged from 0 to 4, targeting specific growth stages: seedling (S), rosette (R), heading (H), and maturity (M). The total number of possible fertilization treatments, 3280, was calculated based on various combinations of these variables. Specifically, the study considered 41 levels of nitrogen application (including 0 kg), five fertilization frequencies, and 16 combinations of four growth stages.

The Treatment ID specifies the amounts of nitrogen (N), phosphorus (P), and potassium (K) applied, the number of fertilization events, and the growth stages (S, R, H, M) at which fertilization was applied. Binary coding (0 and 1) represents various fertilization stage combinations; “1001” signifies fertilization at the seedling and maturity stages. For example, “F50T1001” denotes a treatment with 50 kg·hm⁻² nitrogen, 25 kg·hm⁻² phosphorus, and 50 kg·hm⁻² potassium, applied twice at both the seedling and maturity stages. All treatments used the calibrated CROPGRO model, leveraging 30 years of weather data (1984–2013) to simulate cabbage head yield and leaf nitrogen content. The outputs, head yield and head nitrogen content, function as optimization criteria for fertilization regimes. Optimal fertilization regimes were determined using key performance indicators including head yield, head protein content, and harvest index. Criteria for selecting optimal practices include$$\{\begin{array}{l}\overline{\mathit{Head} \mathit{Yield}} \ge 90\%\mathit{Head} \mathit{Yiel}{d}_{\text{Max}} \\ \overline{\text{Harvest index}} \ge 90\%{\text{Harvest index}}_{\text{Max}} \\ \overline{\text{Head protein content}} \ge 80\%{\text{Head protein content}}_{\text{Max}} \end{array}$$ [6] where head yield is the dry matter weight of cabbage heads, kg·hm⁻²; Head protein content is the percentage of protein in the cabbage heads, %; Harvest index is ratio of head yield to total aboveground biomass, %. $\overline{\mathit{Head} \mathit{Yield}}$ is the average simulated multiyear head yield, kg·hm⁻²; Head Yield_Max is the maximum simulated head yield, kg·hm⁻².

LAI.

Under high fertilizer treatments, the model tends to underestimate LAI growth (Fig. 2A and D). In medium fertilizer treatments, the model demonstrates improved predictive accuracy (Fig. 2B and E). The RRMSE values, 0.084 for 22MF and 0.168 for 23MF, reflect closer alignment with observed values, particularly under medium nitrogen conditions. The model excels in low nitrogen scenarios, as evidenced by strong predictive performance in low fertilizer treatments (Fig. 2C and F). The zero-fertilizer treatment (230F) shows the largest prediction error, with an RRMSE of 0.110 (Fig. 2G). The significant prediction discrepancy underlines challenges in simulating LAI growth in conditions of extreme nitrogen deficiency, necessitating further optimization of model parameters. Overall, the CROPGRO model demonstrates varying degrees of accuracy in simulating LAI for cabbage under different nitrogen treatments.

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Leaf number.

In the 22HF treatment, simulated leaf counts consistently exceeded actual measurements, yielding an RRMSE of 0.092 (Fig. 3A). This overestimation persists through the growth period, notably in later stages, suggesting the model exaggerates leaf growth under high nitrogen conditions. Similarly, for 22LF and 230F, RRMSEs of 0.052 and 0.13, respectively (Fig. 3C and G), indicate the model’s propensity to overpredict leaf growth in low and zero nitrogen scenarios. In the 22MF and 23MF treatments, minor discrepancies between simulated and observed leaf numbers feature RRMSEs of 0.031 and 0.075, respectively (Fig. 3B and E). The lower RRMSEs suggest improved model accuracy under medium nitrogen conditions, likely due to better-calibrated parameters enhancing simulation precision. The 23HF and 23LF treatments display higher simulated than observed leaf counts, though with reduced errors (RRMSEs of 0.083 and 0.024) compared with 2022 (Fig. 3D and F). Especially in early growth stages, closer alignment between simulated and actual values in 2023 demonstrates enhanced model adaptability and prediction accuracy. The 230F treatment exhibits the most significant simulation error with an RRMSE of 0.13, highlighting substantial discrepancies, particularly in later stages (Fig. 3G).

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Tops weight.

For the 2022 high fertilizer treatment (22HF), the model’s simulated biomass closely matched the measured values, demonstrating robust performance with an RRMSE of 0.115 (Fig. 4A). The medium fertilizer treatment (22MF) also showed reasonable accuracy, with an RRMSE of 0.135 (Fig. 4B), whereas the low fertilizer treatment (22LF) achieved the best performance, indicated by the lowest RRMSE of 0.043, exemplifying excellent model precision (Fig. 4C).

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The 23HF treatment showed an RRMSE of 0.066, indicating good alignment between the simulated and observed data (Fig. 4D). The 23MF treatment consistently demonstrated solid performance with an RRMSE of 0.057 (Fig. 4E). However, the 23LF treatment exhibited increased variability with an RRMSE of 0.121, still considered within an acceptable range despite being higher than in the previous year (Fig. 4F). The 230F treatment recorded the largest discrepancy with an RRMSE of 2.744, reflecting significant limitations in the model’s accuracy under conditions of no fertilization (Fig. 4G).

Overall, the CROPGRO model has demonstrated a strong capability in simulating cabbage biomass across various fertilization treatments, with most achieving low RRMSE values that signify good to excellent performance. The notable exceptions in zero fertilization scenarios underscore areas needing refinement. This variability and the consistent performance across different fertilization levels and years underscore the model’s potential utility for agricultural biomass prediction and management.

Head yield.

The 22HF treatment demonstrated close alignment between the simulated and measured head yields, showcasing the model’s robust performance under high-fertilization conditions (Fig. 5). Similarly, the 23HF and 23MF treatments exhibited high accuracy in their predictions, confirming the effectiveness of the model. Although the 22HF and 22MF treatments displayed some discrepancies, their overall performance was satisfactory. However, under severe nitrogen stress conditions (230F), significant deviations between the simulated and observed values highlighted the model’s limitations in accurately predicting yields in extreme scenarios.

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Overall, the CROPGRO model displayed excellent predictive capabilities for cabbage head yield across various fertilization treatments. Despite its strong performance across different fertilization levels and over several years, the model revealed some deficiencies under severe nitrogen stress, pointing to areas for further refinement. The consistent performance across diverse scenarios emphasizes the model’s utility as a valuable tool in agricultural production forecasting.

Head protein content.

The results indicate that the model’s simulated values for head protein content are closely aligned with the measured values across all seven treatments (Fig. 6). This high level of accuracy, with a RRMSE of 0.112, demonstrates the model’s effectiveness in predicting head protein content under varied fertilization regimes. These findings underscore the model’s applicability in optimizing agricultural fertilization management and enhancing crop performance forecasting.

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Fertilization amount.

The optimal fertilization rates to maximize head yield, protein content, and harvest index are ∼180 to 220 kg·hm⁻², 300 kg·hm⁻², and 100 to 140 kg·hm⁻², respectively. Beyond these levels, the benefits of additional nitrogen diminish. Coolong et al. (2022) have shown that optimal nitrogen application significantly enhances cabbage yield up to a threshold, beyond which yields plateau or decline due to potential nutrient imbalances or excessive vegetative growth. As nitrogen application increases, plant roots’ capacity to absorb nitrogen nears saturation, making further uptake challenging (Chun et al. 2005). Moderate nitrogen application optimizes biomass allocation toward economically important plant parts; however, excessive nitrogen may reduce harvest efficiency due to the overgrowth of vegetative parts (Huimin et al. 2020). A combination of factors including nutrient uptake saturation, imbalances, physiological stress, and environmental conditions, limits the efficacy of additional nitrogen, culminating in a plateau or decrease in yield response (Yang et al. 2023).

The CROPGRO model’s performance diminishes under severe stress due to its parameter sensitivity, as calibration tailored for mild stress does not reliably extrapolate to extreme conditions (Boote et al. 1998). Simplifications inherent in modeling stress responses often result in inaccuracies. For example, Ban et al. (2015) pointed out limitations in accurately simulating complex drought responses.

Fertilization frequency.

A typical fertilization schedule includes three to four events per growing season. This frequency ensures continuous nutrient availability, promoting sustained growth, higher yields, and improved nutrient content. Importantly, it avoids the diminishing returns associated with more frequent fertilization. Split nitrogen application has been shown to significantly enhance cabbage yields compared with single or double applications, primarily due to improved nitrogen use efficiency and reduced losses from leaching and volatilization (Qu et al. 2019). Frequent nitrogen applications also increase the protein content in cabbage by ensuring adequate nitrogen availability during key stages of protein synthesis, thereby boosting overall protein accumulation (Zhen-Ming et al. 2013). Furthermore, split applications optimize the harvest index by ensuring a balanced nutrient distribution between vegetative and reproductive plant parts, improving biomass partitioning efficiency (Staugaitis et al. 2008).

Fertilization stages.

Applying fertilizers at the seedling stage is crucial, as it provides young plants with essential nutrients necessary for initial growth. This early nutritional support is pivotal for establishing a robust root system and vigorous vegetative growth, which are indispensable for the plant’s later stages of development. According to Zhang et al. (2012), fertilization at the seedling and heading stages significantly enhances cabbage yields by ensuring the availability of nutrients during critical developmental phases.

Fertilization at the maturity stage has a negligible impact on cabbage yield. Ding et al. (2012) observed that applying nutrients during this phase does not enhance cabbage yield, emphasizing that nutrient absorption is crucial during the early to midgrowth stages. By the maturity stage, cabbage plants have largely completed their nutrient uptake, shifting their focus to head development. Consequently, fertilization at this later stage is ineffective, particularly if the plants did not receive sufficient nutrients during the critical early growth phases, leading to suboptimal development that late-stage fertilization cannot rectify.

In conclusion, the findings indicate that optimal cabbage yields are best achieved by incorporating fertilization during the seedling stage and continuing through multiple growth stages (Fortune et al. 2010). This regime ensures that essential nutrients are supplied from the onset of growth, fostering robust development and enhancing yields. Effective management of the timing and combination of fertilization significantly improves crop productivity (Du et al. 2022).