The study was conducted in Northeast China (38°40′ to 53°34′ N, 115°05′ to 135°02′ E), encompassing Heilongjiang, Jilin, Liaoning provinces, as well as the eastern parts of the Inner Mongolia Autonomous Region (IMAR) (Fig. 1). The study area includes 40 cities and spans approximately 1.24×106 km2. The region is characterized by a continental monsoon climate, with an annual accumulated temperature (≥10 °C) ranging from 2200 to 3600 °C (Pu et al., 2019), and a frost-free period of 140 to 170 d (Tan et al., 2014). The average annual precipitation exhibits a strong east-west gradient, decreasing from 1000 mm in the east to 350 mm in the west (Zhao et al., 2011). The predominant soil types include brown coniferous forest soil, dark brown forest soil, forest steppe chernozem and meadow grassland chernozem soil (Pu et al., 2019). Soybean is one of the three main crops in the region, primarily cultivated in the northern parts of the Songliao plain in rotation with maize. Notably, this region contributes around 64 % of China's total annual soybean production (National Bureau of Statistics of China (NBSC), 2023). Approximately 97 % of the soybean area in the region is rainfed (Guo et al., 2022; Yu et al., 2020), with the growing season typically spanning from May to late September (Zhao et al., 2021).

The soybean growth dataset used in this study was a knowledge-based dataset derived from a crop growth model based on multi-parameter combinations. The dataset provided a quantitative description of yield formation by simulating soybean development under diverse agricultural production scenarios including variations in meteorology (temperature, precipitation, solar radiation), soil types (texture, organic matter), crop varieties (phenology, thermal requirements) and agro-management practices (sowing date).

To generate the dataset, we employed the World Food Studies Simulation Model (WOFOST) (Diepen et al., 1989), implemented via the Python Crop Simulation Environment framework (PCSE, v5.5). The WOFOST model is well-suited for large-scale simulations and has been extensively validated (Huang et al., 2015). Given that soybean cultivation in the study area is predominantly rainfed, we adopted the water-limited mode (Wofost72_WLP_CWB) for simulations. Driven by daily weather data, soil profiles, and cultivar parameters, the water-limited model simulated CO2-driven photosynthesis, water deficits, and biomass partitioning, outputting daily LAI, daily biomass accumulation, and final grain yield. Crop development is modelled through development stages (DVS): 0 for emergence, 1 for anthesis and 2 for maturity (Diepen et al., 1989). This dataset mechanistically captures yield-limiting processes (e.g., drought during critical growth phases) while enabling scalable scenario analysis across Northeast China's rainfed soybean systems.

The Gated Recurrent Unit (GRU) model, a streamlined variant of recurrent neural networks (RNNs), was trained using the simulated soybean growth dataset for large-scale soybean yield estimation. Unlike LSTM (Long Short-Term Memory), the GRU simplifies gating mechanisms to two adaptive gates, update and reset gates (Cho et al., 2014). The update gate retains the past information for future calculations. The reset gate aims to remove irrelevant historical context for simplifying the new candidate hidden states. Using the two gates together is beneficial for balancing long-term dependency capture and computational efficiency (Peng and Yili, 2023; Zhang et al., 2022). This design mitigates vanishing gradient issues while accelerating model training, making GRU particularly effective for time-series yield estimation (Gopi and Karthikeyan, 2023; Ren et al., 2023b).

Trained on the simulated dataset, the GRU model, constructed based on TensorFlow 2.6, linked simulated inputs to yield outputs. For field scale yield estimation, we first identified all available Sentinel-2 observation dates for each sample plot based on its corresponding Sentinel-2 tiles in 2022 and 2023 (Table 4), and computed the development stage value (DVS) for each date (Sect. 3.3.1). As LAI is a key biophysical indicator of soybean photosynthetic capacity and productivity (Ko et al., 2024; Shi et al., 2025), we extracted LAI values at the corresponding DVS from the soybean growth dataset to construct DVS-aligned LAI time series. These DVS-aligned LAI served as inputs to the GRU model, with simulated yield used as the target variable.

However, the spatiotemporal variability of Sentinel-2 image availability across regions posed challenges for regional-scale yield modelling, as constructing separate GRU models for each date combination demands considerable computational and storage resources. Accounting for the computational efficiency of the model in large areas, two stage-averaged LAI, LAI_mean1 (mean value of LAI during vegetative growth: emergence to flowering) and LAI_mean2 (mean value of LAI during reproductive growth: flowering to maturity), were calculated as inputs, while simulated yields acted as outputs. Recent studies have shown that phenology-based feature construction and stage-specific summaries from Sentinel-2 time series can provide an efficient and informative alternative to full-season sequences for crop yield prediction (Gaso et al., 2024; Radočaj et al., 2025). To evaluate the effectiveness of the two stage-averaged LAI in soybean yield estimation, we applied the GRU model trained by the two stage-averaged LAI to yield estimation at the field scale for comparison with the model based on DVS-aligned LAI time series, and further extended its application to the regional scale.

The simulated soybean growth dataset was partitioned using 10-fold cross-validation, with hyperparameters (e.g. learning rate and batch size) optimized using a grid search to achieve minimal root mean squared error (RMSE, Eq. 7) (Açikkar, 2024). Once trained, the GRU model took Sentinel-2-derived LAI as inputs to generate 20 m yield maps.

The accuracy of soybean yield estimation was evaluated on multiple scales. For field scale, in situ yield data in 2022 and 2023 were used for assessment. For regional scale, the average soybean yield for each city and province was separately calculated for each year, and compared with the statistical data. Accuracy evaluation was based on the coefficient of determination (R2, Eq. 6), the root mean squared error (RMSE, Eq. 7) and mean relative error (MRE, Eq. 8). 6R2=1-∑i(yo,i-ym,i)2∑i(yo,i-y‾o)27RMSE=∑i=1n(yo,i-ym,i)2n8MRE=∑i=1n|yo,i-ym,i|n⋅yo,i where yo,i and ym,i represent the actual yield (observed or statistical yield) and model estimated yield, respectively; y‾o is the mean value of the actual yield.

Since LAI was used as the input feature, the accuracy of WOFOST-simulated LAI directly influenced the reliability of the GRU model for soybean yield prediction. To validate simulated LAI, field-measured LAI from 2021 to 2023 were compared with the mean LAI curve calculated from 5000 randomly selected simulated LAI curves from the soybean growth dataset (Fig. 3). The results showed that simulated LAI trends aligned closely with observed field variations, capturing 88 % of the field-measured sample sites (n=83) within the simulated range. This demonstrated robust agreement between model outputs and ground truth, confirming the WOFOST simulations' ability to represent realistic LAI dynamics for GRU training.

Figure 4a displays the histogram distribution of simulated soybean yields, revealing an approximately normal distribution (mean=2675.66 kgha-1). The soybean growth dataset effectively captured a wide range of production conditions, spanning low to high yield extremes. Figure 4b shows a box plot comparing the simulated yield with historical statistics from 1980 to 2022, published yield data from literature, and field measurements from 2022 and 2023. The simulated dataset exhibited the widest value range, demonstrating the comprehensiveness of the multi-scenario knowledge base and the robustness of the simulation outcomes.

The field scale performance of GRU models using full DVS-aligned LAI and two stage-averaged LAI was validated against in situ measurements from 2022 and 2023 (Fig. 5). The estimated yields exhibited strong agreement with observed yield, with R2>0.65 (p<0.01) in all scenarios. Validation results (Figs. 5 and A4) showed that the DVS-aligned GRU model achieved slightly better accuracy (RMSE=224.81 kgha-1, MRE=7.50 %), while the stage-averaged model remained competitive (RMSE=287.44 kgha-1, MRE=10.02 %). The difference in MRE was around 3 % across both years, suggesting that the simplified approach using two stage-averaged LAI was a feasible alternative for yield estimation.

In this study, two stage-averaged LAI (LAI_mean1 and LAI_mean2) were selected as alternative input features to DVS-aligned LAI for soybean yield estimation. Although full LAI sequences yielded higher accuracy at local scale (Figs. 5 and A4), their regional application was limited by (a) strong spatiotemporal heterogeneity of Sentinel-2 image availability (Fig. A1), which required constructing a specific time-series input for each site individually, and (b) substantial computational and data-management costs related to model training and maintenance for many different sequence-patterns. The two stage-averaged LAI features provide a computationally efficient solution for regional yield mapping, while full time-series inputs offer modest accuracy gains that are best exploited at local scales or where dense, regular observations are available.

For further analysis, we systematically evaluated a broad set of candidate features derived from LAI, transpiration (TRA), and surface soil moisture (SM) extracted from the simulated soybean growth dataset. To develop a unified model suitable for long-term and large-scale soybean yield estimation, we employed statistical summaries of these features rather than time-series features tied to specific image acquisition dates (as done by Du et al., 2025). For each variable, four statistical descriptors – including mean, maximum, median, and cumulative sum – were calculated separately for the vegetative growth stage, the reproductive growth stage, and the whole growing season, following the approach of Ren et al. (2023b).

As shown in Fig. 11, LAI-derived features exhibited consistently strong correlations with simulated yield (r=0.54 to 0.88), reflecting the role of LAI as a critical proxy for canopy development, light interception, and biomass accumulation (Cao et al., 2025; Shi et al., 2025). Multispectral LAI retrieval therefore effectively characterizes both canopy structure and physiological status, supporting its dominant predictive power in our feature set.

Notably, the two stage-averaged LAI (LAI_mean1 and LAI_mean2) exhibited stronger correlations with yield than features derived from either single phenological stage or the entire growing season, which is consistent with Ren et al. (2023b). Conceptually, LAI_mean1 captures vegetative vigor (establishment and biomass accumulation, Kodadinne Narayana et al., 2024), while LAI_mean2 reflects reproductive canopy status. These two features jointly summarize the two most yield-informative phases and mitigate the redundancy present in full sequences. Among the candidate features, mean-based features outperformed maximum, median, and cumulative counterparts. This is likely due to their lower sensitivity to extreme values and day-to-day fluctuations, making them a more stable and representative indicator of canopy conditions across the two growth periods.

While some TRA-based features (e.g., TRA_sum) showed relatively high correlation with yield, they were excluded owing to practical constraints. Current TRA retrieval methods primarily rely on thermal-infrared remote sensing, which typically has coarse spatial and temporal resolution (Anderson et al., 2024; Hou et al., 2018) limiting its utility for high-resolution, regional mapping. Similarly, SM-related features showed weak or inconsistent correlations with yield across growth stages in our simulations, indicating a limited direct influence on soybean yield formation under modelled conditions.

In summary, to optimize model inputs for efficient, large-scale applications, and to facilitate the generation of a soybean yield dataset, the two stage-averaged LAI features (LAI_mean1 and LAI_mean2) were selected. This selection balances physiological relevance and temporal specificity with strong predictive performance and practical feasibility, enabling competitive yield estimation using only two interpretable, remotely sensed retrievable predictors.

This study generated soybean yield estimates using both MODIS LAI (500 m) products and Sentinel-2-derived LAI (20 m) data. Over 2019–2022, the MODIS-based estimates achieved an overall R2 of 0.58 (p<0.01), an RMSE of 272.36 kgha-1 and a MRE of 12.08 % (Fig. 12b), slightly lower than the Sentinel-2-based results (Fig. 12a). The uncertainty of MODIS-based estimates was higher than that of the Sentinel-2-based estimates, likely reflecting MODIS's coarser resolution. However, the Sentinel-2-based estimates exhibit inherent seaming effects caused by cloud-affected tile edges. We additionally used MODIS LAI to bias-correct Sentinel-2 yield maps, effectively minimizing the striping (“seaming”) effects in the 20 m products (Fig. 9), while preserving pixel-level detail through tile-based calibration. Despite differences in spatial resolution, both MODIS and Sentinel-2 satellite data demonstrated comparable ability to capture spatiotemporal variation in soybean yield (Fig. 13), achieving correlations with statistical data >0.55 and overall errors <13 % across all years.

In practical applications, balancing both temporal and spatial resolution is critical for achieving robust yield prediction results (Azzari et al., 2017). Figure 14 compares the Sentinel-2 yield maps and the MODIS LAI yield maps within a 10 km grid under different soybean coverage. Thanks to 4 d revisit, MODIS LAI provides more cloud-free observations during the critical growth stages, improving the reliability of two stage-averaged LAI (LAI_mean1 and LAI_mean2). Its coarser spatial resolution also accelerates spatial processing over large areas. However, Sentinel-2's finer spatial resolution more effectively resolves intra-field yield heterogeneity (Fig. 14). MODIS-derived maps occasionally underestimated yields due to mixed pixels containing non-crop features (e.g., infrastructure), whereas Sentinel-2 minimized such errors.

While this study prioritized high-resolution mapping (using MODIS solely for Sentinel-2 seam correction), combining high-spatial-resolution data (e.g., Sentinel-2 or UAV imagery) with high temporal frequency satellites (e.g., geostationary sensors or radar) could provide an optimal data source for crop-yield modelling (Gao and Anderson, 2019; He et al., 2018).

Accurate monitoring of soybean yield is crucial for food policy decision-making and security assessment. While previous studies have primarily explored the impact of environmental factors such as climate on soybean productivity (Guo et al., 2022; Zhao et al., 2023a), few efforts have focused on producing high-resolution soybean yield datasets for China's major soybean-producing regions. To address this gap, our study produced the NortheastChinaSoybeanYield20m dataset, a 20 m resolution dataset generated through a hybrid framework integrating the mechanistic WOFOST crop growth model and a GRU deep learning algorithm. Unlike purely data-driven approaches that rely on extensive ground data, our approach leveraged both data mining capabilities and mechanistic modelling, which improves the model's interpretability and enhances its potential for transferability across regions. The integration of the WOFOST model ensured the simulation of diverse production conditions under varying climate, soil, crop variety and management conditions, providing a robust synthetic training dataset for the GRU network. This combination allowed the model to perform well, even in areas with limited observational data, therefore overcoming common limitations related to data scarcity and high computational costs. Accuracy assessments using both in situ and statistical yield data confirmed that the generated NortheastChinaSoybeanYield20m dataset delivered reliable yield estimates across field and regional scales (Figs. 5 and 6). The results also verified the model's stability across time and space, reinforcing its potential for large-scale agricultural monitoring and strategic planning.

When compared to previous studies using integrated remote sensing data and a process-based model to estimate soybean yield, for instance, Baup et al. (2015) reported estimation errors ranging from 2 % to 18 %, our method achieved comparable levels of accuracy. It also outperformed existing field-scale studies (e.g., RMSE=400.946 kgha-1 in Ren et al., 2023a, and MRE of 29.73 % in Du et al., 2014) and municipal-scale models (e.g., MRE=16% in Von Bloh et al., 2023). Furthermore, the NortheastChinaSoybeanYield20m dataset showed improved performance relative to similar high-resolution soybean yield products from other countries (e.g., annual 30 m soybean yield mapping in Brazil, with R2 values between 0.31 and 0.71 and RMSEs ranging from 275 to 740 kg ha⁻¹) (Song et al., 2022).

Although studies based on UAV and RGB data have demonstrated even higher soybean yield estimation accuracy (Li et al., 2021, 2024), such methods are often constrained by high costs and limited spatial coverage, making them impractical for large-scale applications. In contrast, the method developed in this study offers a well-balanced solution that combines computational efficiency, high spatial resolution, and strong predictive accuracy. Our approach offers a scalable and practical solution for producing high-resolution, large-scale crop yield datasets.

In this study, a soybean growth dataset was developed by simulating various combinations of input parameters within the WOFOST model. These diverse parameter combinations were designed to reflect different environmental and management conditions, ultimately serving as training data for the yield estimation model. One advantage of the model is its scalability: it can be readily applied to other regions and countries that lack sufficient ground observation data, such as parts of Africa and India, thus offering a promising tool for global agricultural monitoring.

However, the validation results revealed some notable limitations. Specifically, the model exhibited a tendency to produce high uncertainty in low- or high- yielding areas, introducing error into the overall yield estimation (Figs. 5 and 6). This pattern suggests a systematic bias in the model's predictions, particularly in regions with extreme yield values. Additionally, spatial analysis showed that estimation errors were more pronounced in the northern region, which is characterized by complex terrain, compared to the relatively flat central region (Fig. 7). These discrepancies highlight the need to refine parameterization for extreme yield conditions and integrate higher-resolution environmental drivers (e.g., terrain, localized weather).

First, the estimation errors may be attributed to the inherent limitations of the WOFOST model. As a process-based model, WOFOST simplifies its calculations for simulating physiological processes, which can hinder its ability to fully replicate the complex realities of soybean in the field. Factors such as pest infestations, diseases, and abiotic stresses are either oversimplified or excluded (Gaso et al., 2024). These omissions can lead to systematic simulation errors, particularly under stress conditions that significantly affect crop yield. Moreover, the parameterization of the WOFOST model in this study purely relied on values from literature and existing datasets rather than site-specific optimization against independent observations. As a result, local variability because of farming practices, soil properties, and environmental conditions may not have been adequately captured. This lack of local optimization likely resulted in higher estimation error, especially in complex landscapes with sparse ground observations. For future studies, the use of targeted field-measured and remotely sensed products (e.g., surface soil moisture, solar-induced chlorophyll fluorescence (SIF), LiDAR-based biomass, and leaf chlorophyll content), integration of advanced data assimilation approaches (e.g., assimilating SIF or leaf chlorophyll content) and model sensitivity analyses will further increase biological realism. Moreover, given the spatial variability in soybean growth within the study area, constructing ecological zones based on factors like climate, elevation, and management practices might provide a more targeted model approach. For instance, Huang et al. (2023) defined ecological zones using Theissen polygons derived from meteorological station locations. This zoning strategy could enhance the representativeness of the training data and reduce yield estimation uncertainties.

Second, the estimation errors may stem from the overfitting of the GRU model. The GRU was trained on the simulated soybean growth dataset, a large number of simulations that included all available combinations (e.g., all meteorological data), which introduced a significant amount of redundant information. The redundancy not only potentially reduced the dataset's representativeness, but also increased the computational burden during model training. As a result, the trained GRU model may have become overly tuned to specific temporal patterns in certain years, limiting its ability to generalize to other time periods or regions with different growth conditions. This overfitting effect might result in large yield estimation errors across different years and regions, particularly in areas where soybean yields deviated significantly from the norm. To address these issues, refining the structure and composition of the training dataset, and removing redundant information would enhance the diversity and quality of the training inputs. One potential approach to reduce redundancy is through spatiotemporal clustering of environmental variables (e.g., meteorological station data), which could filter out stations with highly similar information. Moreover, monitoring the validation error throughout the training process, and implementing regularization techniques (e.g., L2 weight regularization) could help to prevent overfitting and improve the GRU model's generalization capability, leading to improved soybean estimation across varying conditions.

Third, using the two stage-averaged LAI introduces additional sources of uncertainty in yield estimation. Excessive temporal aggregation inevitably obscures growth dynamics. Different growth trajectories can produce similar stage-based LAI yet correspond to different yields, increasing the risk of non-unique relationships between LAI and spatial yield patterns. This simplification also limits the modelling capacity of GRU architectures, which are specifically designed to exploit sequential dependencies in time series inputs. Future work could explore hybrid approaches that combine stage-based summaries with higher-frequency or full-season time series of vegetation indicators to improve both interpretability and yield prediction robustness. In addition, future model extensions could consider architectures specifically designed for irregular or missing sequential observations, such as GRU-D or Transformer-based approaches (Che et al., 2018; Chen et al., 2022b). These models may provide a more flexible way to capture temporal dependencies under non-uniform observation intervals and could further improve the robustness of soybean yield estimation in data-sparse conditions. On the other hand, errors in LAI retrieval from remote sensing data also contributed uncertainty to yield predictions. The published LAI–NDVI_RE relationship is broadly transferable because red-edge-based VIs are less sensitive than traditional VIs (e.g., NDVI, CI_green and EVI) to variations in canopy structure, phenology, and site locations (Dong et al., 2019; Nguy-Robertson et al., 2014; Viña et al., 2011). Red-edge-based VIs (e.g., NDVI_RE) also mitigate soil-background influences. Nevertheless, the modest overestimation we observe at low LAI indicates that residual soil-background differences between our Northeast China sites and the original Spanish and Italian calibration plots can still bias the regression under sparse canopies. Directly applying the published LAI–NDVI_RE regression without regional re-calibration may therefore propagate bias into yield estimates. Integrating agronomic knowledge with remote sensing mechanisms has emerged as a promising way to reduce uncertainty and improve model reliability (Chen et al., 2022a; Hu et al., 2024). In future work, coupling radiative transfer models such as PROSAIL (Jacquemoud et al., 2009) with a crop growth model would allow the direct use of satellite reflectance and is expected to reduce bias from site-specific LAI regressions and further improve model accuracy (Ntakos et al., 2024).

Finally, the combination of IoT, blockchain, and precision agriculture with machine learning and biophysical models can offer a powerful framework for sustainable agricultural monitoring, addressing challenges in data heterogeneity, model scalability, and decision-making processes. These technologies can facilitate real-time data collection, ensure data security and transparency. Precision agriculture techniques, combined with advanced sensing technologies, can effectively improve the accuracy and timeliness of input data, addressing current limitations in model calibration, validation and prediction.