The North China Plain (Fig. 1) features a warm temperate continental monsoon climate, characterized by abundant sunlight and warmth, although precipitation is unevenly distributed, with the majority falling during the summer months (June to August). The predominant soil type in the North China Plain is aeolian soil deposited over geological periods by rivers. This study focuses on wheat cultivation in the North China Plain, the second-largest plain in China, which plays a crucial role in grain production. The dominant cropping system in this region is a double-cropping system of winter wheat and summer maize. To ensure data quality and integrity, we selected 25 counties for this research (Fig. 1). Table S1 in the Supplement provides detailed information on the crops and climate at these research stations.

The phenological period simulation results for the 25 sites in the study area showed good performance in both the calibration and validation datasets (Fig. 4, Tables S5 and S6). In the calibration dataset (Fig. 4, Table S5), the WOFOST model's RMSE for heading ranged from 1.4 to 12.8 d, with an average of 5.7 d. The best-performing site was Jiexiu, while the worst-performing site was Fengyang. For the maturity period, the RMSE ranged from 3.1 to 13.1 d, with an average of 8.0 d. In comparison, The WOFOST-EW model's RMSE results for heading and maturity periods were 4.2 and 5.4 d, respectively.

In the phenological simulation results for the validation dataset (Fig. 4, Table S6), the RMSE for heading and maturity periods using the WOFOST model ranged from 1.0 to 9.5 d (average of 4.7 d) and from 3.2 to 11.8 d (average of 7.0 d), respectively. For the WOFOST-EW model, the RMSE for heading date simulations ranged from 1.0 to 6.0 d, with an average of 4.2 d, while for maturity date simulations, the RMSE ranged from 3.2 to 8.0 d, with an average of 6.1 d. The best and worst-performing sites for heading and maturity dates simulations using the WOFOST-EW model were Bazhou and Shenzhou, and Laiyang and Shenzhou, respectively.

Figure 4c and d present box plots of the RMSE for heading and maturity dates simulated by the WOFOST and WOFOST-EW models. In the validation dataset, for the heading date, the lower and upper quartiles for the WOFOST model were 3.8 and 5.5 d, respectively, while for the WOFOST-EW model, they were 3.9 and 4.7 d (Fig. 4c). For the maturity date, the lower and upper quartiles for the WOFOST model were 5.4 and 7.7 d (Fig. 4d), while for the WOFOST-EW model, they were 4.6 and 7.0 d. These results indicate that, compared to the WOFOST model, the proposed WOFOST-EW model significantly reduced the RMSE for both heading and maturity dates, thus improving accuracy. Furthermore, the smaller interquartile range suggests a narrower error range, indicating more stable and precise simulation results.

During the validation period, the original WOFOST model exhibited an RRMSE of 4.61 % for heading and 4.74 % for maturity, with R2 of 0.53 and 0.45 (p<0.05), and MAE of 4.4 and 5.6 d, respectively (Fig. 4). In contrast, the improved WOFOST-EW model substantially enhanced phenological simulation performance, achieving lower RRMSEs of 3.74 % (heading) and 3.98 % (maturity), higher R2 values of 0.69 and 0.56 (p<0.05), and reduced MAEs of 3.8 and 5.3 d, respectively (Fig. 4). These results indicate that WOFOST-EW improves both the accuracy and precision of phenological predictions. Based on the evaluation using the validation dataset, the RMSE for heading simulation is reduced by 10.64 %, and for maturity by 12.86 % (Fig. 4).

Despite some differences in simulation results across counties, the WOFOST model's simulated yields aligned well with observed yields (Figs. 5, 6, and 7, Tables S5 and S6). In the calibration dataset, the average RMSE in the simulated counties was 673.01 kg ha⁻¹ (RRMSE = 16.66 %) (Figs. 5 and 6, Table S5). Among these, Dingxiang performed the best, with an RMSE of 355.83 kg ha⁻¹ (RRMSE = 9.75 %), while Changli showed poorer results, with an RMSE of 844.58 kg ha⁻¹ (RRMSE = 21.38 %). For the validation dataset, the RMSE of simulated yields by the WOFOST model ranged from 256.61 to 938.19 kg ha⁻¹, with an average RMSE of 665.76 kg ha⁻¹ (RRMSE = 13.55 %) (Figs. 5 and 6, Table S6).

The improved WOFOST-EW model more accurately simulated winter wheat yields from 1980 to 2020 (Figs. 5, 6, and 7, Tables S5 and S6). In the calibration dataset, the RMSE for yield simulations ranged from 295.63 to 758.14 kg ha⁻¹, with an average of 541.90 kg ha⁻¹ (RRMSE = 13.60%). In the validation dataset, the RMSE ranged from 279.64 to 960.75 kg ha⁻¹, with an average of 565.63 kg ha⁻¹ (RRMSE = 11.30 %).

From 1990 to 2020, a comprehensive evaluation of annual yield simulations by the WOFOST model was performed (Fig. 6). The WOFOST model utilized a set of optimal parameters obtained through the SCE-UA method, allowing for effective simulation of wheat yields. During the verification period, in the WOFOST model, the MAE of the simulation results was 566.08 kg ha⁻¹ (MRE = 12.09 %), while the WOFOST-EW model reduced the MAE to 463.82 kg ha⁻¹ (MRE = 10.11 %) (Fig. 6). Despite the overall high accuracy, errors were identified in yield simulations for certain years (Fig. 6b).

To further evaluate the performance of the two models, we analyzed the results for the validation dataset from 2001 to 2020 (Fig. 7). The simulation results of the WOFOST model showed a Pearson's r of 0.83 and an R2 of 0.67 (p<0.01). In comparison, the WOFOST-EW model demonstrated enhanced yield estimation accuracy, with a Pearson's r of 0.86 and an improved R2 of 0.76 (p<0.01) (Fig. 7). In addition, we compared the annual distribution of traditional extreme weather indices with the extreme weather function values F(EW) proposed in this study (Fig. 8). We used 1 - F(EW) to represent the intensity of extreme weather impacts on crop growth. The results indicate that in years with extreme climatic conditions, this metric exhibits higher values, reflecting stronger weather-induced stress on crops. Conversely, in years with relatively normal climate conditions, F(EW) values remain stable, suggesting limited impact. These findings demonstrate that the model effectively captures and quantifies the influence of extreme weather on crop development.

To further evaluate the effectiveness of the improved model, we conducted yield simulations at specific sites affected by extreme weather events. Based on prior reports, the years 2009, 2010, 2012, and 2018 were selected for modeling analysis under extreme weather conditions. Detailed information on the agricultural meteorological experimental stations impacted during these events is provided in Table S2.

According to the Ministry of Ecology and Environment of the People's Republic of China (https://www.mee.gov.cn, last access: 3 February 2024), the study region experienced record-breaking high temperatures in 2009, with several locations breaking previous historical records. In 2010, the frequency of meteorological disasters increased, with numerous extreme weather events reported. In 2012, China experienced 38 heavy rainfall events, 21 of which occurred during the summer. Some regions were hit by exceptionally extreme weather events, most notably the “7.21” event (Zhao et al., 2019b). Additional disasters – including droughts and cold waves – also occurred during this period (Zhao et al., 2019b; Zheng et al., 2018). In 2018, extreme low-temperature events caused frost damage, significantly affecting agricultural productivity (China Meteorological Administration, https://www.cma.gov.cn, last access: 10 January 2024). These extreme events in the selected years contributed to significant yield reductions in the study area (Figs. 6 and 8)

In the four experimental years (Figs. 9 and 10, Table S7), WOFOST produced simulation results with a Pearson's r ranging from 0.81 to 0.87 (p<0.01), an R2 of 0.61 to 0.71 (p<0.01), an RMSE of 781.56 to 1043.28 kg ha⁻¹ (RRMSE of 16.22 % to 23.83 %), and an MAE of 654.78 to 871.20 kg ha⁻¹ (MRE of 14.07 % to 26.65 %). In comparison, WOFOST-EW achieved a Pearson's r of 0.91 to 0.94 (p<0.01), an R2 of 0.80 to 0.86 (p<0.01), an RMSE of 555.72 to 711.38 kg ha⁻¹ (RRMSE of 11.53 % to 16.25 %), and an MAE of 372.25 to 587.84 kg ha⁻¹ (MRE of 8.21 % to 19.15 %). Overall, WOFOST-EW demonstrated higher simulation accuracy.

In the WOFOST model, crop responses to temperature are represented by the function F(T) (Eqs. 2–5), which is simple and intuitive in form. Within the optimal temperature range, F(T) can approximate a linear relationship between temperature and crop development rates. However, it exhibits notable limitations in capturing the nonlinear stress effects associated with extreme temperature conditions.

First, the model does not account for the suppressive impacts of heat stress. When temperatures exceed the upper threshold Tm, F(T) remains constant, implying that crops cease to respond to further temperature increases. This overlooks the detrimental effects of extreme heat, such as inhibited photosynthesis, elevated respiration rates, and damage to reproductive organs, potentially leading to an overestimation of crop growth under high-temperature conditions. Second, the model oversimplifies cold stress. When temperatures fall below the base temperature Tb, the development rate is set to zero. While this indicates a conceptual halt in growth, it fails to differentiate between varying intensities of cold stress and their distinct physiological impacts on crops.

To address these limitations, this study introduces an extreme weather function F(EW), which incorporates the cumulative and phenological-stage-specific impacts of stressors such as heat, drought, and heavy precipitation. This function dynamically adjusts phenological development and enhances the model's sensitivity to extreme climatic events. Importantly, F(EW) does not replace F(T) but complements it – offering a more comprehensive framework for assessing the effects of climate extremes and climate change on crop production.

Extreme weather events – such as heatwaves, frosts, droughts, and floods – have substantial impacts on crop growth and yield (Lüttger and Feike, 2017; Xiao et al., 2018; Zahra et al., 2021). Wheat phenology is particularly sensitive to meteorological factors like temperature and moisture, and extreme weather often leads to stage-specific disruptions in its developmental process (Asseng et al., 2015; Sadras and Monzon, 2006; Tao and Zhang, 2013; Zahra et al., 2021). In the North China Plain, both HDD and LDD fluctuate considerably during the winter wheat growing season, reflecting frequent exposure to severe heat and cold stress. This is consistent with previous findings indicating that winter wheat is often subject to extreme low temperatures prior to flowering and extreme high temperatures afterward – both of which significantly reduce yield (Bai et al., 2024). Studies have shown that elevated temperatures tend to shorten the wheat growing period, particularly affecting the sowing-to-flowering phase (Asseng et al., 2015; Li et al., 2020b; Sadras and Monzon, 2006; Tao and Zhang, 2013; Zahra et al., 2021). During early growth stages, moderate warming can enhance thermal accumulation and stimulate photosynthetic enzyme activity, promoting leaf area expansion and chlorophyll synthesis, and thereby accelerating heading and flowering (Chen et al., 2014; Li et al., 2020b; Tao et al., 2017a; Tao et al., 2017b). However, high temperatures following flowering can trigger premature leaf senescence and reduced photosynthetic capacity, leading to early maturity and shortened grain-filling duration (Harrison, 2021; Liu et al., 2023). Conversely, extreme low temperatures – particularly frost – can significantly delay development. Frost events may damage young spikes and floral organs, disrupting reproductive development (Fuller et al., 2007), while cold stress during the vegetative stage can cause visible injuries such as leaf tip burn (Shroyer et al., 1995). Rapid temperature drops are more damaging than gradual cooling (Al Issawi et al., 2013; Li et al., 2014b) and can impair organ formation even without reaching lethal thresholds. Cold stress also suppresses metabolic activity and delays cell division and elongation, especially prolonging the jointing-to-heading interval (Xiao et al., 2021). If such events occur during spike differentiation, they can lead to spikelet abortion or sterility, posing a severe threat to final yield.

Although drought or water stress is not typically the primary factor influencing phenology, it can still exert a significant impact in drought-prone regions (McMaster and Smika, 1988; McMaster and Wilhelm, 2003). The effect of drought depends on its timing, intensity, and the crop's developmental stage, often resulting in either accelerated development or developmental arrest (Chachar et al., 2016; Ihsan et al., 2016). Wheat has evolved several drought-resistance strategies to cope with water stress, including drought escape (accelerating the life cycle to avoid drought periods), drought avoidance (e.g., regulating stomatal behavior to minimize water loss), and drought tolerance (maintaining cellular function under stress conditions) (Nyaupane et al., 2024). While these adaptive responses enhance survival and confer a degree of yield stability, they are often associated with a shortened developmental cycle and advancement of phenological phases (Chachar et al., 2016; Chowdhury et al., 2021; Ihsan et al., 2016; McMaster and Wilhelm, 2003). Extreme precipitation events can also disrupt wheat development, primarily through waterlogging. Under flooded conditions, oxygen deficiency in the root zone inhibits root elongation and nutrient uptake (Chachar et al., 2016; Chowdhury et al., 2021; Ihsan et al., 2016; McMaster and Wilhelm, 2003), and in severe cases, may cause root death (Herzog et al., 2016). Additional negative effects include reduced root front expansion (Ebrahimi-Mollabashi et al., 2019), nutrient leaching (Kaur et al., 2020), and impaired water transport, all of which contribute to stomatal closure and diminished photosynthetic activity (Jitsuyama, 2017). Waterlogged conditions also elevate the risks of lodging and disease outbreaks (Nguyen et al., 2016). While most research has focused on the impacts of waterlogging on crop growth and yield, there is increasing recognition of the need to understand its effects on crop phenology (Nóia Júnior et al., 2023). Empirical studies have shown that waterlogging during critical early stages such as tillering and jointing can significantly suppress chlorophyll synthesis and photosynthetic capacity, impeding early growth and potentially delaying or disrupting subsequent phenological stages, including jointing and heading (Dickin and Wright, 2008; Wu et al., 2015).

Phenological stages play a crucial role in determining crop yield, and the phenological process itself serves as a primary pathway through which extreme weather influences crop production (Chachar et al., 2016; Chowdhury et al., 2021; Ihsan et al., 2016; McMaster and Wilhelm, 2003). However, most current crop models struggle to accurately simulate phenology under extreme conditions and often fail to capture phenological shifts induced by extreme weather events (Zhang and Tao, 2019). Enhancing the accuracy of phenology prediction under such conditions is therefore essential for overcoming key limitations in crop models and improving their ability to simulate crop performance under climate extremes (Pei et al., 2025). In this study, we employed seven climate indices to quantify extreme climate conditions and observed spatial variability in the impacts of extreme weather across different counties (Fig. 8). Against the backdrop of global warming, future changes in the frequency and intensity of extreme weather events may pose increasing risks to wheat production.

The uncertainty of crop model parameters is a complex and significant issue, with limited empirical data on crop development rates under extreme temperature conditions being a key factor. Previous studies have shown that the parameters of temperature response functions largely depend on field experimental data; however, these data often lack coverage of extreme temperature environments (Bai et al., 2022b; Ellis et al., 1992; Tollenaar, 1979; Watts, 1971; Zhang and Tao, 2019). A recent study (Zheng and Zhang, 2025b) highlighted that the rising frequency of extreme weather events leads to increased variability and unpredictability in meteorological observations (e.g., temperature and precipitation). Such variability complicates the derivation of stable and representative input parameters (e.g., thermal time, stress thresholds) for crop models, thereby introducing uncertainty into model simulations (Gao et al., 2020, 2021). This instability may lead to deviations in model outputs, ultimately affecting the accuracy of crop growth predictions. Additionally, obtaining reliable crop simulation parameters under extreme weather conditions is highly challenging. For instance, in the North China Plain, frequent high and low-temperature extremes can disrupt the consistency of daily weather inputs used in models (Gu et al., 2024). This inconsistency affects the reliability of key model parameters (e.g., effective temperature accumulation, phenological thresholds), ultimately reducing the accuracy of crop growth and yield simulations under such extreme conditions (Bai et al., 2024).

To address these challenges, we developed the WOFOST-EW model to better quantify the impacts of extreme weather events. This improved model demonstrated lower uncertainty and reduced fluctuation in simulation results. The phenological simulation results (Fig. 4) and yield simulation results (Figs. 5–7) showed that the improved model simulated crop growth more accurately, reducing bias and increasing the model's reliability.

In this study, we developed the F(EW) function, leveraging climate indices and LSTM algorithms, and successfully integrated it into the WOFOST model. The results demonstrate that the WOFOST-EW model significantly enhanced yield prediction accuracy in the counties impacted by extreme weather events (Figs. 9 and 10). By incorporating climate indices, the model achieves improved accuracy in predicting heading dates, maturity dates, and yield. After an evaluation of simulations from 1990 to 2020, the WOFOST-EW model demonstrated superior predictive accuracy. These findings confirm that the F(EW) function is a robust approach for enhancing model performance. Future research could explore its potential applications across other crops and regions to broaden its utility. Further analysis revealed that the WOFOST-EW model excelled in simulating wheat yields under extreme climate conditions. Notably, extreme weather events in 2009, 2010, 2012, and 2018 presented significant challenges for traditional modeling approaches. However, by integrating climate indices and LSTM algorithms, the improved model achieved a substantial enhancement in simulation accuracy (Figs. 9 and 10). The extreme weather correction factor F(EW) developed in this study relies on the complete growing-season weather sequence to capture stage-specific crop responses, enhancing end-of-season yield simulation. This dependence limits its use for in-season forecasts when future weather data are unavailable. Future work could address this by generating scenario-based F(EW) from seasonal forecasts or ensemble predictions, coupled with data assimilation to update it dynamically during crop growth.

Previous studies have attempted to estimate the impacts of extreme weather events on crop yields using machine learning approaches. However, many of these studies have relied on outputs from crop models as inputs to machine learning algorithms, rather than directly modeling the weather-crop relationship (Feng et al., 2019a; Li et al., 2023; Shahhosseini et al., 2021; Zhuang et al., 2024). The key innovation of our model lies in the integration of an extreme weather function, F(EW), which enhances the ability of the model to capture the dynamic effects of extreme weather events on wheat yields. This theoretically improves prediction accuracy while maintaining a strong physiological basis. The WOFOST-EW model performs robustly not only under general climatic conditions but also under extreme weather scenarios, owing to the responsiveness and spatial-temporal specificity of the F(EW) variable. Moreover, WOFOST-EW exhibits broad applicability and holds potential for extension beyond the North China Plain to other regions and crop types. Future research could further improve the model by incorporating additional environmental and management-related data to enhance its adaptability and predictive accuracy under diverse conditions. Nevertheless, the physiological diversity across crops – including differences in growth cycles and environmental responses – presents challenges for direct transferability of the model. While WOFOST is a generic crop simulation model, its current structure and parameters are particularly well-suited to cereal crops. Application to crops with fundamentally different morphological or physiological characteristics (e.g., root vegetables, oilseeds, or perennials) would require substantial recalibration and structural adjustments. Additionally, although the LSTM-based deep learning component of WOFOST-EW lacks the biological transparency of traditional physiological models, the hybrid design enhances the model's explanatory power regarding extreme weather impacts. Regional variation in crop growth due to differences in climate, soil properties, and management practices further underscores the need for localized parameter calibration when applying the model to new regions or crop types. Currently, the F(EW) function in WOFOST-EW focuses primarily on meteorological stressors. However, crop performance is also influenced by complex and interacting non-meteorological factors such as soil fertility, pest and disease outbreaks, irrigation, and fertilization practices. This study assumes that crop growth is not limited by nutrient availability, it cannot reflect the dynamic regulatory effects of fertilization management and may underestimate the potential interactions between nutrient stress and climatic factors. A key direction for future development is the integration of these additional stressors – particularly sudden biotic pressures or severe nutrient limitations – and their interactions with extreme weather into the WOFOST-EW framework. Such advancements would further strengthen the model's realism and utility for decision-making under climate extremes.

During validation, the WOFOST-EW model underperformed in several counties (Fig. 5). Further investigation revealed that the primary reason for this was that, due to data limitations, we only accounted for the heading and maturity stages and omitted other key phenological periods of winter wheat. In addition, the F(EW) generated by the model is a season-scale scalar correction factor, which is applied to the calculation of crop development rates throughout the entire growing period. This incomplete consideration of growth stages likely impacted the model's ability to fully capture the crop's growth dynamics under varying conditions. Previous studies have shown that the effects of extreme climate events on crop production vary across different growth stages (Feng et al., 2019b; Porter and Gawith, 1999; Tack et al., 2015). During the wheat growth cycle, different stages experience varying types and intensities of climatic stress, resulting in significant differences in yield impacts. Moreover, severe droughts occurring during the critical growth stages from April to May are particularly likely to affect winter wheat yields (Xu et al., 2018; Yang et al., 2020). Additionally, a series of studies on different crop types and regions have demonstrated that crop yields are more vulnerable to droughts occurring during key growth stages (Pena-Gallardo et al., 2018; Potopova et al., 2015; Zipper et al., 2016). This phenomenon can be attributed to two main factors: (1) physiological differences and variations in field management practices across phenological stages (Wu et al., 2004), which result in distinct drought resistance capacities at different growth stages (Nesmith and Ritchie, 1992); and (2) the varying impacts of droughts on yield formation depending on the growth stage at which they occur (Zhao, 2001). This presents an important direction for future research and model improvement. By further refining the model to account for specific types and intensities of climatic stress at different growth stages, we can enhance prediction accuracy and better capture the impacts of extreme weather events on wheat yields.