This study was implemented during 2015–2018 at the Xiaotangshan National Precision Agriculture Research Centre (40.17°N, 116.43°E), positioned on the outskirts of Beijing, China (Figure 1a), a site well-known for precision farming research. The local site, characterized with warm temperate and semi-humid climate with a continental monsoon pattern, features silt loam soil with 0–30-cm-layer properties with concentrations of NO₃⁻-N (3.16–14.82 mg kg⁻¹), NH₄⁺-N (8.12–14.52 mg kg⁻¹), organic matter (15.8–20.0 g kg⁻¹), available phosphorus (3.14–21.18 mg kg⁻¹) and exchangeable potassium (86.83–120.62 mg kg⁻¹). The maximum temperature is 38.8 °C in summer, and the minimum temperature is -20.5 °C in winter. The annual amount of solar radiation and precipitation is 4850 MJ m⁻², and 400–620 mm respectively (China Meteorological Data Service, http://data.cma.cn/).

Experiments 1 (2015–2016) and 2 (2017–2018) (Figure 1b) were identically designed as two-factor randomized complete block designs. The two winter wheat varieties tested were Luanxuan 167 and Jingdong 18. N application rates included four levels: 0 kg N ha⁻¹ (N1), 90 kg N ha⁻¹ (N2), 180 kg N ha⁻¹ (N3) and 270 kg N ha⁻¹ (N4). Urea was used as the N source and applied in equal amounts during the seeding and jointing stages. All other management practices adhered to local agricultural standards. There were 32 plots per growing season, with 128 biomass samples (32 plots × 4 periods) and 32 yields collected annually. The data from Experiments 1 and 2 were used for parameter calibration of the recommended fertilization model in this study. These data was used to set up DSSAT simulations with different fertilization rates during the jointing stage for target yield analysis.

Experiment 3 (2017–2018) was conducted during the 2017–2018 growing season, testing two wheat varieties (Luanxuan 167 and Jingdong 18). A base application of 90 kg N ha⁻¹ of N fertilizer was applied, with subsequent topdressing based on a data assimilation system during the jointing stage: T0 (no topdressing), T1 (25% of the recommended rate), T2 (50%), T3 (75%), T4 (100%) and T5 (125%). There were 32 plots with 128 biomass samples (32 plots × 4 periods) and 32 yields collected. Base fertilizers included 375 kg ha⁻¹ of calcium superphosphate and 150 kg ha⁻¹ of potassium sulfate. All other agronomic practices followed local farming standards. Experiment 3 was used for model validation.

AGB measurements were conducted at key growth stages of winter wheat: stem elongation, flag leaf emergence, flowering, and grain filling. At each developmental stage, 20 stems of winter wheat were randomly selected from every experimental plot. After isolating the individual plant parts, the stems underwent a 30-minute heat treatment at 105 °C, followed by oven drying at 80 °C until reaching a stable mass. The final dry mass of each sample was then recorded. The aboveground dry biomass (AGB, t ha^-1) was determined based on the stem count per hectare at each growth phase using the Equation 1:

where AGB refers to aboveground dry biomass measured in tons per hectare, D indicates the dry mass in grams, and n stands for the number of stems per hectare across different growth stages. The values 15 and 20 represent the conversion factors for per-mu and per-hectare, and the conversion factor for dry weight to above-ground dry biomass, respectively (Zhao et al., 2025).

At harvest, a 1 m² standard sampling plot was established within the experimental field. All plants within the plot were harvested, and the grain dry weight was determined after threshing and oven drying. Afterward, the yield was normalized to a moisture content of 14% and converted to a per-hectare value (t·ha⁻¹).

Meteorological data, including daily precipitation and maximum and minimum temperatures, were obtained from the China Meteorological Data Sharing Service System (CMDSSS, https://data.cma.cn). Solar radiation was calculated using the Angström–Prescott formula described by Allen et al. (1998), based on the sunshine duration recorded in CMDSSS.

A quadcopter UAV (Phantom 4 Pro, DJI, China) was used to collect remote sensing data under favorable weather conditions, specifically clear skies, no wind, and no cloud cover, with all flights adhering to the same take-off points and flight paths to ensure uniformity. Missions were conducted at 12:00 PM, maintaining a flight altitude of 30 m, with 80% forward and 85% lateral overlap. Prior to image acquisition, reflectance data from a spectral calibration panel were recorded to correct the pixel brightness values in the multispectral images. Orthomosaics were generated using Pix4Dmapper 4.3. Additional details on the image processing workflow can be found in Yang et al. (2021). The spectral characteristics of the sensor are illustrated in Figure 2b.

In this study, the enhanced vegetation index 2 (EVI2), a widely adopted spectral index in vegetation monitoring, was employed to estimate AGB, following the formulation proposed by Jiang et al. (2008). The index is calculated using Equation 2:

where NIR and R are the reflectance values in the near-infrared (NIR) band (840 nm) and red band (650 nm), respectively. The constants 2.5, 2.4 and 1 are the correction factors to mitigate the influence of soil background, atmospheric interference and signal saturation, thereby enhancing the sensitivity of the index in densely vegetated areas.

A data assimilation framework was developed to optimize N fertilizer recommendations by integrating a crop growth model with UAV remote sensing data (Figure 3). Particle swarm optimization (PSO) is an efficient algorithm inspired by bird flock foraging behavior. Particles adjust their positions based on individual and group experience, with fast convergence and few parameters, making it widely used for crop model parameter optimization (Yi and Ge, 2005; Elbeltagi et al., 2005). This study uses the PSO algorithm for remote sensing data assimilation in the DSSAT (CERES-Wheat) model to optimize crop parameters and recommend N fertilization. The initial soil nutrient contents, including NO₃^--N and NH₄⁺-N, were obtained from field measurements and used to initialize the DSSAT model. In this study, variations in management practices were appropriately considered during the data assimilation process to simulate crop responses under different management scenarios within a unified parameter framework. Meanwhile, in the simulation of recommended fertilization, top-dressing parameters at the jointing stage were adjusted to analyze top-dressing amounts and target yields under different nitrogen treatments, thereby optimizing the recommended fertilization rates and accurately reflecting crop growth, the specific steps are as follows: First, AGB estimation of winter wheat was conducted based on UAV remote sensing data. Second, AGB data assimilation modeling was performed using the Particle Swarm Optimization (PSO) algorithm. Third, the assimilation algorithm optimized the DSSAT model using the fertilization plans of each experimental plot to ensure that the simulated yields closely matched the target yields for the respective test fields.

The DSSAT model was calibrated by adjusting AGB to match observed growth and yield measurements. Model evaluation was based on field experiment data, using a stepwise parameter adjustment approach to minimize simulation errors. During the validation phase, independent experimental data were used to assess model performance, primarily through statistical metrics such as R² and nRMSE, to quantify the agreement between simulated results and observed data, ensuring the model’s applicability and reliability under different growing seasons and management conditions. The model’s performance was quantified by the adjusted determination coefficient (R²) and relative root mean square error (nRMSE), with better performance being indicated by a higher R² and a lower nRMSE. The formulas for calculating R², RMSE, and nRMSE are shown in Equations 11, 12, and 13, respectively.

where n, Y′_i, Y_i and p represent the sample size, estimated value, measured value and number of predictors, respectively. In subsequent sections, R² for the calibration and validation sets are denoted as R²_c and R²_v, respectively; nRMSE for these sets are represented as nRMSE_c and nRMSE_v.

In this study, the winter wheat AGB ranges for the training and validation datasets were 1.84–14.14 t ha⁻¹ and 0.84–15.44 t ha⁻¹, with mean values of 7.27 t ha⁻¹ and 5.93 t ha⁻¹, respectively (Figure 4). To mitigate the effects of growth stages on AGB remote sensing monitoring, this study integrated EVI and growth stage information employing the HLM for winter wheat AGB inversion. Inversion results indicated that the HLM performed excellently, with R²c and R²v values of 0.94 and 0.82 and nRMSEc and nRMSEv values of 13.62% and 15.42%, respectively (Figure 3, Table 2). These results demonstrate the high accuracy of the HLM in AGB inversion for winter wheat, providing reliable estimates for subsequent N diagnosis.

The amount of simulated AGB under different N fertilizer treatments based on the DSSAT model increased with the advancement of growth stages. AGB accumulation increased with increasing N fertilizer rates (Figure 5), while the difference between N3 and N4 treatments was relatively small. This suggests that excessive fertilization has a limited effect on crop yield improvement. Therefore, N fertilizer recommendations should balance both economic and ecological benefits. The amount of simulated AGB at various growth periods closely corresponded to the measured AGB, with nRMSE values of 11.20% and 19.44% for the calibration and validation datasets, respectively (Figure 6a). Similarly, the yield results simulated by the DSSAT model showed good agreement with the observed data, with nRMSE values of 6.35% and 11.12% for the calibration and validation datasets, respectively (Figure 6b).

This study explores how crop income responds to different N topdressing rates under fixed basal N levels (N1–N4), with total N topdressing rates ranging from 0 to 360 kg ha^-¹ (Figure 7). When fertilizer costs are not considered, total income increases with the amount of fertilizer applied, indicating that higher N application can boost crop yield and, consequently, total income. Specifically, the total income reached its maximum at a fertilization rate of 360 kg ha⁻¹ under N1, N2, N3 and N4 treatment levels. However, maximizing income without considering fertilizer costs does not reflect the actual profit for farmers. Specifically, the optimal fertilization rates for N1, N2, N3 and N4 treatments are 140 kg ha⁻¹, 120 kg ha⁻¹, 80 kg ha⁻¹ and 40 kg ha⁻¹, respectively (Figure 7). In practical agricultural production, farmers should find a balance between fertilizer application and its cost to optimize net income. Therefore, the study highlights that while increasing fertilizer application can enhance crop income, excessive fertilization may lead to high costs that reduce net income, making it crucial for farmers to use an appropriate amount of fertilizer to maximize profitability.

The N topdressing rate recommended by the data assimilation system are primarily determined based on the growth status of the crop and exhibits a significant correlation with AGB at the jointing stage (Figure 8). This relationship is described by a quadratic function y = 92.61x^-0.88, with R² of 0.65. A relatively low AGB indicates weak crop development, necessitating a higher N rate. The spatial distribution maps of AGB and N topdressing rates based on UAV remote sensing data and DSSAT model are shown in Figure 9. The results reveal the spatial variability of crop growth status and nutrient requirements in the study area, providing data support for the implementation of variable-rate fertilization management.

In the recommended fertilization trial area (Experiment 3), wheat yields ranged from 3.00 t ha⁻¹ to 8.08 t ha⁻¹. Crop growth simulation models indicate continuous yield generally increases with higher fertilization rates. Therefore, this study selected 125% of the data assimilation-based recommended fertilization amount (T5) as the control treatment. The average yields for treatments T0, T1, T2, T3, T4 and T5 were 4.73 t ha⁻¹, 5.47 t ha⁻¹, 5.50 t ha⁻¹, 5.71 t ha⁻¹, 6.46 t ha⁻¹ and 6.52 t ha⁻¹, respectively (Figure 10). The yield of treatment T5 was slightly higher than that of T4 with no significant difference, but the yields of both treatments were significantly higher than those of the other treatments. For economic benefits, treatment T4 slightly outperformed T5 with no significant difference, and both treatments achieved significantly higher economic returns than the other treatments. This suggests that while optimizing fertilization plans, a moderate reduction in N input can still maintain high yield levels, providing a cost-effective and efficient fertilization strategy for agricultural production. In practical applications, appropriate N fertilization not only promotes crop growth but also reduces the risk of environmental pollution.

Data assimilation algorithms not only offer clear advantages in estimating the current crop state but also demonstrate strong robustness and dynamic adaptability in forecasting later growth stages. This research employs AGB as the assimilation variable, which is vital for formulating accurate fertilization strategies. Li et al. (2024) also employed AGB as a state variable for data assimilation in N recommendation for rice. The AGB monitoring model based on HLM achieved calibration and validation R² values of 0.94 and 0.82 with nRMSE of 13.62% and 15.42% and provided notable scalability throughout the growing season (Figure 2, Table 2). The jointing stage, as the key period for winter wheat topdressing, is highly sensitive to management practices. This study demonstrates that the N topdressing rate recommended by the data assimilation system exhibits a negative power-law relationship with aboveground biomass (AGB) at the jointing stage of winter wheat (R² = 0.65), a pattern analogous to the critical nitrogen dilution curve (Justes et al., 1994). This relationship arises primarily because (1) plots with higher AGB have sufficient N accumulation and thus require less additional N input, whereas plots with lower AGB are relatively nitrogen-deficient and require greater N compensation., and (2) spatial heterogeneity in soil nutrients and water results in differences in crop growth potential, necessitating location-specific adjustments of recommended fertilization even under uniform management practices. Previous studies using growth indicators such as leaf area index and nitrogen nutrition index for fertilizer recommendation have also obtained similar results (Xue et al., 2008; Li et al., 2024b). This study developed an empirical curve linking biomass to recommended nitrogen application, but it was constructed using data from a specific experimental field. With the accumulation and optimization of more data, this approach has the potential to evolve into a simple fertilization recommendation tool, serving as a practical alternative to complex data assimilation systems.

The setting of target yields should not solely focus on maximizing yield, as this may lead to excessive use of N fertilizer, resulting in environmental issues such as soil acidification and groundwater pollution (Peng et al., 2010). In this study, target yield is constructed based on economic benefits. The calculation of target yield considers not only the final crop yield but also the relationship between fertilizer costs and yield gains. Data assimilation-based fertilization decisions driven by target yield allow for the balancing of yield, costs and profits, thus maximizing economic benefits. The recommendation to enhance N application in fields with poor crop growth and reduce it in fields with robust growth is in agreement with the results from previous research (Zhang et al., 2022). Additionally, data assimilation-based N recommendation methods facilitate the precise achievement of target yields and quantify N fertilizer recommendations for heterogeneous growth zones within fields (Figures 7, 9). In this study, the optimal fertilization rates for N1–N4 treatments (140, 120, 80, and 40 kg ha^-¹) follow a trend consistent with previous research (Yang et al., 2022; Li et al., 2024a).

Simulation results indicated that, compared with traditional fertilization strategies, this method maintained relatively stable yields while reducing N application by 6.69%–34.08% (Figure 10). Therefore, the target yield-based data assimilation strategy holds potential to become a practically applicable approach for fertilization optimization (Wang et al., 2023). Setting target yields depends largely on historical data and predictive models, which can introduce errors, particularly in the face of significant climate variability. To address these uncertainties and to evaluate the environmental benefits of reduced N application, future research integrating field measurements with modeling approaches is essential for guiding sustainable fertilization practices.

Significant progress has been made in N recommendation methods using data assimilation systems; however, numerous challenges remain concerning their widespread adoption and practical application in agriculture. This research primarily focuses on growth differences in winter wheat caused by nutrient factors and does not consider other influencing factors such as pest and disease stress. The acquisition and quality control of multi-source observational data are primary issues in current N fertilizer recommendation systems (Lu et al., 2022). The effectiveness of data assimilation heavily relies on the accuracy, frequency and spatial coverage of observational data. Issues such as insufficient temporal resolution, limited spatial precision and meteorological interference limit the precision required for N management (Diacono et al., 2013). The uncertainty in remote sensing observations is introduced into the assimilation process, and misleading parameter corrections may occur when observational errors are combined with model biases (Kang and Özdoğan, 2019). This study realized N fertilizer recommendation applications based on UAV data, offering spatial and temporal flexibility, thereby establishing a technically robust and economically feasible pathway for precision agriculture applications. In the future, integrating the spatial advantages of satellite remote sensing data will further enhance the cost-effectiveness and practicality of large-scale precision agriculture applications.

This study not only validates the potential of data assimilation in crop N management but also identifies the directions for the further improvement of model reliability. However, the predictions of a single crop growth model are inherently uncertain (Huang et al., 2017; Zare et al., 2024). The combination of multiple models can effectively address the shortcomings of a single model’s adaptability in specific scenarios, further advancing the application and development of data assimilation technology in agricultural management (Huang et al., 2017; Zare et al., 2024). Existing research indicates that model integration or weighted averaging methods can reduce biases that may arise from a single model. Among studies comparing algorithms that include PSO, most show that PSO outperforms other methods in terms of convergence speed, computational efficiency, and assimilation accuracy. However, some studies report that PSO is not the best-performing algorithm, indicating that algorithm performance depends on the specific study context, assimilation variables, and model complexity (Table 3). This study selected the PSO algorithm as the data assimilation method, which has demonstrated good performance in assimilating initial input parameters and simulating grain yield (Wang et al., 2024). The PSO algorithm can operate with a simple encoding scheme and achieves higher retrieval accuracy for nitrogen application rates (Wang et al., 2014). In this study, PSO was applied for fertilizer recommendation, yielding stable results. Future research should compare fertilization strategies developed using multiple assimilation algorithms to identify more accurate assimilation methods for more rational fertilization strategies.