The impacts of temperature averages, variabilities and extremes on China’s winter wheat yield and its changing rate

China is the world’s largest producer and consumer of wheat. The impact of temperature averages, variabilities, and extremes on winter wheat yield changes is still not very clear. The annual production data for winter wheat in China’s provinces and municipalities and NCEP-NCAR Reanalysis-1 data were used from November to April in the period 1949–2018, to investigate the impact of temperature-related variables, such as the winter average temperature ( T2m¯ ), winter variance of temperature ( T2m_var ), extreme hot days (EHD), and extreme cold days (ECD), on China’s winter wheat yield. Ensemble Empirical Mode Decomposition (EEMD) analysis showed that winter wheat yield has an in-phase relationship with average temperature but an out-of-phase relationship with variance of temperature, extreme hot days, and extreme cold days on timescales greater than 20 years. The changing rates of winter wheat yield and temperature-related variables were well measured by their sliding trends. At the overwintering growth stage, the increasing rate of average temperature and extreme hot days (temperature variance and extreme cold days) exhibit negative (positive) correlations with the rate of winter wheat yield change, with the strongest correlation observed in southeast China. During the tillering growth stage, the changing rates of average temperature exhibited a positive correlation with the rate of winter wheat yield change, whereas negative associations were observed with temperature variance, extreme hot days, and extreme cold days. Among the regions, Central China showed the weakest correlations. At the reviving growth stage, however, the relationship of changing rates of temperature-related variables with that of winter wheat yield was much weaker. These observational results are important and can be used as a reference in climate models for improving the climatic impacts on the winter wheat yield.


Introduction
Human-induced climate warming is anticipated to have a marked negative impact on crop production (Piao et al2010, Godfray et al 2010, Xiao et al 2018, IPCC 2021. The yield of wheat, one of the top three global cereals, is reported to be reduced by about 5.5% in major grain-producing regions from 1980 to 2008, relative to a counterfactual without climate trends (Lobell et al 2011). This reduction, when excluding the impacts of CO 2 fertilization, effective adaptation, and genetic improvement, translates into a reduction of 4.1 to 6.4% for every 1°C rise in global average temperature (Liu et al 2016, Zhao et al 2017. Via a spatially detailed global assessment of the links between historical climate variability and yield, Ray et al (2015) found that the interannual variations of temperature variability influence wheat yield variability widely in South Asia, parts of Western Australia, South Australia, and Queensland, most of Eastern Europe and many regions of Western European countries.
However, it is less clear for the impact of warming on winter wheat yields in China, which is the world's largest producer and consumer of wheat (Zhang et al 2013, Zhu et al 2018 and more pronounced warming in winter has been observed (Fan et al 2021, Chen et al 2009, Liang et al 2014. Positive and negative mixed temperature impacts have been reported (Liu et al 2016, Chen et al 2018, Zhu et al 2018. Heat stress from tassel to maturity was on the rise in most of the winter wheat-producing regions in China but the South suffers more negative impacts than the North , Tao et al 2014, Chen et al 2018, Zhu et al 2018, Zhu et al 2018, Y Lobell et al 2011, Zhang et al 2021. Some provinces in the north experienced increased grain production due to rising average and minimum temperatures (Meng et al 2013, Ye et al 2020, Zhang et al 2021. Global warming also brought about changes in temperature variance, extreme hot days (EHD), and extreme cold days (ECD) (Alexander 2016). Particularly, the annual average number of EHD increases, while the number of ECD decreases (Yan et al 2002, Qian and Lin 2004, Zhang et al 2004, Zhang and Qian 2008, Zhou and Ren 2011. When the temperature variance and extremes increase, it can hinder photosynthesis and reduce wheat yield (Shi et al 2012, Salazar-Gutierrez et al 2013, Shi and Shi 2016. For instance, extreme heat can strongly reduce the winter wheat yield through excessive heat stress, especially in South China Zhai 1998, Liu et al 2014).
Moreover, crops including winter wheat at different growth stages have different levels of sensitivity to climate change (Yu et al 2018, Balla et al 2019, Liu et al 2023. The growth period that has a significant impact on winter wheat yield can be divided into the tillering stage (early November-mid-December), the overwintering stage (late Decemberlate February), and the reviving stage (March-early April). The period of each stage varies from place to place, but it can basically be represented by such a stage division (http://www.agri.cn/kj/nyqxqb/, http://www.nmc.cn/). During the tillering and reviving stages, winter wheat is more sensitive to temperature, while it's more resistant to cold during the overwintering period (Cai and Jiang 2013, Zhu et al 2008, Guo andHuang 2009). Therefore, a discussion of specific growth stages is necessary when exploring the temperature impacts on winter wheat yield.
Most existent studies explored the impact of global warming on winter wheat yield through model simulations (Rosenzweig et al 2013 and linear regressions (Chen et al 2014, Ray et al 2019, Wang et al 2022. Nevertheless, numerical models are not always able to capture the complicated actual situation and the correlation or linear regression between raw data, which contain information on linear trends due to different reasons, is not sufficiently convincing. This study, therefore, starts from provincial raw data and examines the relationships in the long-term trends, variations at different timescales, and sliding trends between various temperature-related variables and winter wheat yields, to reveal the possible impact of temperature averages, variabilities and extremes in winter on the winter wheat yield in China and its changing rate at various timescales. Results obtained in this study would have profound implications for guiding future modeling endeavors.

Study area and datasets
Based on annual production data for various grain types in China's provinces and municipalities, the winter wheat yield in each year was obtained. Restricted by local climatic conditions, not all provinces in China are suitable for planting winter wheat. For example, due to its cold winters, only spring wheat was planted in the Northeast. Therefore, we focus on changes in the mid-year winter wheat yield in the provinces where winter wheat is grown, namely Xinjiang, Hebei, Henan, Anhui, Jiangsu, Gansu, Ningxia, Shanxi, Shaanxi, Sichuan, Guizhou, Hunan, Hubei, Zhejiang, Guangdong, Fujian, Yunnan, Guangxi, and Jiangxi (see figure S1 in Supplementary Information).
The meteorological data used was the daily mean 2m air temperature field derived from the NCEP-NCAR Reanalysis-1 dataset during the growth stages of winter wheat (1 November-10 April) from 1948 to 2018. We considered four temperature-related variables that were possibly related to the winter wheat yield over its growing region: the average temperature over the period (denoted as T 2m ), the variance of the daily temperature over the period (denoted as T 2m_var ), and the number of days per year accounted for by the front and back 5% of the daily temperature over the period (denoted as EHD and ECD, respectively).
To further investigate the relationship between temperature-related variables and winter wheat yield in China, three critical growth stages of winter wheat, namely, the tillering stage, overwintering stage, and reviving stage, need to be considered as these stages are highly influenced by climatic conditions. However, this is challenging given a lack of historical detailed information regarding the crop growth stages for various provinces in China. Weekly updates on the current growth stage of winter wheat since November 2021 at major production provinces only are provided at the website http://www.agri.cn/kj/nyqxqb/zb/index.html provides. Based on the time range of growth stages derived from the limited information available as shown in figure 1, this study defines the start and end times of the three growth stages for winter wheat in the main production regions of China as follows: the tillering stage from November 1st to December 20th (the start and end dates of the tillering stage for 70% of the available records fall within this defined period), the overwintering stage from December 21st to February 29th (86% of the available records fall within this defined period), and the reviving stage from March 1st to April 10th (72% of the available records fall within this defined period).

Methods
Ensemble Empirical Mode Decomposition (EEMD) was applied to the time series data of winter wheat yield and related meteorological variables and then found their relationship at different timescales. This method is suitable for the processing of nonlinear and non-stationary signals, and the result processed by this method has a Figure 1. The start and end dates of winter wheat developmental stages for various major production provinces in China according to the data available at the http://www.agri.cn/kj/nyqxqb/zb/index.html. (a), (b), and (c) represent the corresponding start and end dates of tillering, overwintering, and reviving stages for the respective major production provinces. The x-axis represents the start dates of the developmental stages, while the y-axis represents the corresponding end dates. The color dots with numbers indicate the number of cities with the same corresponding developmental period. relatively high signal-to-noise ratio (Huang et al 1998, Huang et al 1999, Battista et al 2007, 2009, Wu and Huang 2009). Using the EEMD method, the original time series can be divided into a limited number of Intrinsic Mode Functions (IMFs) and a residual variable (Gaci 2016). The residual is always considered as the non-linear trend of the time series (Gaia, Giorgio (2015), Agbazo et al 2021). Each IMF component contains the local features of the original time series at different time scales, while the characteristics of the original data are preserved as much as possible.
Sliding trend analysis (STA) was applied to trend subsequences in different time scales. Starting from 1949, the data values in the continuous period were selected, and the trend value of the intercepted data values over a specific time window was calculated. The intercepted time series of a variable x can be denoted as where i is the year when the data was intercepted, and j is the number of years in this continuous time window (j = 11, 39). Therefore, the sliding trend value (ST ij ) for the time window starting from the year i to year i+j is derived as the linear trend of time series X . ij By considering the sliding trends, we aim to capture the underlying relationship between the change rate of winter wheat yield and temperature-related variables within various time window, which can also naturally remove the impact of the long-term trends that might be related to nonclimatic factors on the temperature-winter wheat yield relationship.
Empirical Orthogonal Function (EOF) analysis (Weare and Nasstrom 1982) and K-means cluster analysis (Edwards and Cavalli-Sforza 1965, Blashfield and Aldenderfer 1978, Mahlstein and Knutti 2009, Carvalho et al 2016 were conducted on the decadal-multi-decadal components of yearly and provincial winter wheat yield field derived from EEMD method to partition China into several regions based on the provincial winter wheat yield from 1949 to 2018. Note that the winter wheat yield is influenced by not only climatic factors but also other factors such as economic development and technological changes that help increase the crop yield in the long term (Qin et al 2015, Li et al 2019, Wang et al 2020. The region division based on the temporal-spatial changes of the decadal-to-multi-decadal components, rather than the total field, of the winter wheat yield may reflect the climatic effects better. After such region division, we can investigate the common features of temperaturerelated variables corresponding to the changes in winter wheat yield in the specific region that may be related to climate.

Results
3.1. China's total winter wheat yield and temperature conditions over the entire China 3.1.1. Temporal evolution and long-term linear trends As seen from figure 2, China's national total winter wheat yield and T 2m showed an increasing trend throughout the study period. The T _ 2m var and EHD showed a clear upward trend after 1990. The ECD also showed large values in recent decades. The winter wheat yield exhibited an in-phase trend with the T 2m from 1948 to 2018 and with T _ 2m var and EHD since around 1990. However, these correspondences in trends do not indicate any causality between wheat yields and these temperature-related variables, as they may vary for different reasons. The increasing winter wheat yields might be also closely related to China's economic development and various agricultural practices. The increase of T 2m was consistent with global warming (Zhou and Wang 2000), which has also led to more EHD and fewer ECD in winter.
The correlation analysis revealed that, regardless of whether detrending was applied or not, the correlation coefficients between the time series of winter wheat yield and the four temperature-related variables did not pass the 95% significance level. Nevertheless, small correlations do not necessarily deny the potential link between year-to-year changes in winter wheat yields in China and these temperature-related variables. Given the multifaceted and intricate nature of factors influencing winter wheat yield variability, relying solely on linear trends and correlation analyses of observational data may be insufficient to fully capture the possible connections.

Ensemble empirical mode decomposition components
We used the EEMD method to non-linearly decompose the time series of China's winter wheat yield, T , 2m T _ , 2m var EHD and ECD, calculated the cross-correlations among various IMF and residual components, as shown in figure 3, to investigate their possible linkage among components at different timescales as well as among their non-linear trends.
Firstly, the residual IMF component reveals a non-linear long-term trend, and it demonstrates a positive correlation between the residual component of China's winter wheat yield and that of T , 2m while exhibiting negative correlation with that of T _ , 2m var EHD and ECD. This confirms the general in-phase trend between winter wheat yield and winter mean temperature as shown in figure 2 but an out-of-phase trend of the yield with winter temperature variance and extremes in the long period from 1949 to 2018. On the multi-decadal time scale (>20 years), the IMF 3 of winter wheat yield, with a dominant period of 28 years, shows a similar relationship with temperature-related variables as the residuals, except for the correlation between winter wheat yield and EHD, which becomes insignificant (figure 3(c)). On the interannual time scale (<10 years), the winter wheat yield shows insignificant correlations with four temperature-related variables in most cases, except for a positive correlation between EHD and winter wheat yield at a period of 6-8 years but become negatively correlated at a period of 2 years. Therefore, the relationship between China's national total winter wheat yield and the four temperature variables has varied significantly with their time scales of variability over the past 70 years.

Sliding trends analysis
The decomposed time series plots shown in figures S2-S6 yield that the relationship between the variations of winter wheat yield and temperature-related variables can vary depending on the time windows. For example, the in-phase correspondence between the trend of winter yield and trends of T _ , 2m var EHD and ECD is only observed after the 1990s. In addition, the changing rate of these variables that can be measured by sliding trend may provide a more informed perspective on the potential connection between China's total winter wheat yield and various temperature conditions, as it contains less information on long-term linear trends as well as cumulative impacts.
) of winter wheat production areas in the period from 1st November of the previous year to 10 April of the current year, from 1949 to 2018. 'k' and 'p' represents the slope and significance of the regression lines respectively.
The changing rate of winter wheat yield was overwhelmingly positive, keeping an increasing trend from 1949 to 2008 (figure 4(a)). The winter wheat yield's sliding trend with an 11-year window exhibited a decline to its minimum value below zero in the late 50s, then it recovered to be positive and reached its first and largest peak in the early 1970s, followed by a second peak in the late-1980s. Since the 1990s, the growth began to slow down, although there was a slight acceleration slightly after the mid-1990s. As the window interception period expands, the temporal evolution of the sliding trend also showed similar features despite being more leveled off, showing one relatively fast-increasing period around 1965-1985 and two relatively slow-increasing periods, which were before 1965 and after 1985.
Comparing figure 4(a) with the temporal evolution features of sliding trends of temperature-related variables (figures 4(b)-(e)), the T _ , 2m var EHD and ECD showed positive sliding trends, particularly after 1985-1990, which is consistent with the positive trend of winter wheat yield in the same period. But this relatively fast-increasing period for the three temperature-related variables, with larger positive values of sliding trends, corresponded to the relatively slow-increasing period of winter wheat yield. This might suggest negative impacts from temperature conditions on the winter wheat yields in terms of their changing rate.
The sliding trends indicating the changing rates of all four temperature-related variables were mainly negatively correlated with that of the winter wheat yield (figure 4(f)). Specifically, for T , 2m the significance was concentrated around the decadal scale (11-14 years). As the scale of the sliding window increased, the negative correlation gradually dropped and approaches zero near 28 years. For ECD (T _ 2m var and EHD), however, the negative correlations were significant for sliding windows of periods longer than 20 (30 years), reaching their strongest negative correlations at around a 35-year window. The ECD has the most pronounced negative correlation with winter wheat output, peaking at −0.75. This indicates that the accelerated increases in the T _ , 2m var EHD and ECD in winter over 2 to 3 decades correspond well to the slowing down of the growth rate of winter wheat yield. The relationship between the changing rates of temperature-related variables and winter wheat yield, rather than themselves, was more consistent with previous statements on the impact of extreme temperatures on winter wheat yield, suggesting the usefulness of STA in finding observational evidence.
Further dividing the winter season into three stages corresponding to wheat growth, the close relationship between the sliding trend of T 2m and that of winter wheat yield was found during the tillering and overwintering stages ( figure 5(a)). Specifically, the correlations were significantly positive for the tillering stage at the multidecadal window, with a maximum reaching in the 33-year window. The correlations during the overwintering stage ( figure 5(a)), however, are negative from decadal to multi-decadal windows. This suggests that the relatively strong cold resistance of winter wheat and the negative impacts from warming during the wintering period. The sliding trends of T _ , 2m var EHD and ECD exhibit a significant relationship with that of the winter wheat yield mainly at the overwintering stage. On the one hand, the changing rate of T _ 2m var and ECD were positively correlated with that of winter wheat yield, indicating the positive impacts of several rounds of cold temperature events with wintery precipitation on the winter wheat growth at the overwintering stage. On the other hand, the changing rate of EHD at the overwintering stage was negatively correlated with that of winter wheat yield at multi-decadal time windows longer than 25 years.

Region-dependent relationships in terms of sliding trends
China's extensive territory and significant climatic variations between regions prompted us to investigate the region-specific impacts of temperature on the growth rate of winter wheat yield. Considering that the significant relationship between temperature-related variables and winter wheat yield, we extract the components of winter wheat yield fields at timescales from decadal to multi-decadal. And then we applied the K-means clustering analysis for the objective reference to region division that might be related to temperature conditions. Based on this analysis, we divided the winter wheat growing region into three subregions, as illustrated in   6(a)). EOF analysis was also applied to justify the rationality of the region division (figure S7).
Seen from figures 6(f), (j), and (n), the negative correlations between the sliding trend of winter wheat yield and those of T _ , 2m var EHD, and ECD in the entire winter are more significant for each of the three regions compared to the China total (figure 4(f)), while the T 2m exhibits significant negative correlations only in Region I ( figure 6(b)). This indicates that the negative impact on winter wheat yield from larger temperature variability is in all regions of China, while that from higher winter mean temperature is mainly in southeastern China.
A closer examination of the region-dependent correlations of sliding trends at each specific growth stage reveals that at the tillering stage, the positive correlations of winter wheat yield with T 2m and negative correlations with T _ , 2m var EHD, and ECD are strong in Region I and III but weakest in Region II, where they are significant only at windows longer than 30 years (figures 6(c), (g), (k), (o)). At the overwintering stage, as shown in figures 6(d), (h), (l), and (p), the negative impacts from T 2m and EHD and positive impacts from T _ 2m var and ECD are significant in almost all the three regions (except for the insignificant relationship between T _ 2m var and winter wheat yield in Region II) but strongest in southeastern China (Region I). From figures 6(e), (I), (m), and (q), we see that the correlations between the sliding trends of temperature-related variables and winter wheat yield are weakest at reviving stage, with no clear regional differences. The only significant negative correlations are found with T _ 2m var in Region I. Therefore, the response of winter wheat growth to temperature conditions at the tillering and overwintering stages can be modulated by the local climate, giving rise to remarkable regional differences in the temperature impacts on the winter wheat yield across China.

Discussions
It is important to note that our results show clearly that the winter wheat yield and winter temperature variance and extremes generally exhibit out-of-phase trends and multi-decadal changes in the period from 1949 to 2018, from the EEMD analysis. And in addition, the STA analysis suggests that the escalated increments in winter temperature variance and extremes over two to three decades align with the deceleration of the growth rate in winter wheat yield. These results provide more evidence from different perspectives for the previous statement about the negative impact of extreme temperatures on winter wheat yield. According to Yadav (2010), extreme Figure 5. Correlation coefficients between sliding trends of regional winter wheat yield and regional mean (a) T , 2m (b) T _ , 2m var (c) EHD, (d) ECD during the tillering stage (November 1-December 20), overwintering stage (December 21-February 29) and reviving stage (March 1-April 10). Open (solid) circles represent correlations above the 99% (95%) significance level. cold can increase the likelihood of low-temperature disasters, causing mechanical injury and metabolic dysfunction of winter wheat, thus stunting its growth. Extreme heat can reduce winter wheat yield by intensifying the heat stress in the form of dry-hot winds and quick maturing of winter wheat during the growing season (Ren and Zhai 1998, Balla et al 2009, Feng et al 2019. In addition, since the heat stress between tassel and maturity has increased over the last few decades in most of China's major winter wheat-producing areas , the extreme heat is considered as the largest challenge for agriculture and crop production (Ren and Zhai 1998, Salazar-Gutierrez et al 2013). Thus, our results confirm the adverse impact of extreme temperatures Figure 6. (a) Three-region division according to the K-means clustering of decadal-to-multi-decadal component of China's yearly provincial winter wheat yield. Correlations between sliding trends of regional winter wheat yield and regional mean (b-e) T , 2m (f-i) T _ , 2m var (j-m) EHD, (n-q) ECD during the whole growth period, tillering, overwintering and reviving stages for each region. Open (solid) circles in (b-e) represent correlations above the 99% (95%) significance level. on winter wheat yield in terms of trends, multi-decadal scale variability, and changing rates over two to three decades.
Our findings further suggest that the effects of temperature on yield are indeed highly dependent on the growth stage, highlighting the importance of considering growth stage-specific impacts when considering the agricultural responses to climate change. In particular, the changing rate of T 2m shows a positive relationship with the winter wheat yield during the tillering stage but negative relationship found during the overwintering stage. This could be attributed to the relatively strong cold resistance of winter wheat during the wintering period, and a sufficiently long period of low temperature during its growth phase can help prevent premature transition to a more cold-affected growth stage, as reported by Kosová et al (2008). Once the temperature rises, the emergence of seedlings becomes slow and the cold resistance declines Therefore, the increase in T 2m may have a negative impact on the winter wheat yield at the overwintering stage. Winter wheat in other growth stages has weaker cold resistance (Cai and Jiang 2013), so the impact of accelerated increasing T 2m turns to be positive. The T _ 2m var and ECD exhibit a positive relationship with yield during the overwintering stage, suggesting that multiple cold temperature events with wintery precipitation have a beneficial impact on winter wheat growth during this stage. The appropriate cooling in winter contributes to the accumulation of dry matter in wheat and enhances its resistance to certain pests and diseases, according to previous studies Moreover, the regional dependence of the relationship between the STA of winter wheat yield and winter mean temperature is suggested by our analysis. In Region I (mainly including southeastern China), the changing rate of T 2m exhibited a most significant negative correlation with that of the winter wheat yield among all regions. This may be attributed to the higher levels of pre-existing heat stress in the southern regions . The rising average temperature aggravates the original heat stress, exerting a negative impact on winter wheat yield. Contrarily in the other provinces, this situation will reduce the probability of freezing damage and offset part of the heat stress caused by the temperature rise, thus exerting a weak impact on the changing rate of winter wheat yield. During the tillering stage, the correlation between the sliding trend of winter wheat yield and that of temperature variability appears to be weakest in Region II. This could be attributed to the fact that compared to Regions I and III, Region II primarily encompasses the majority of Northwestern and North China, located in the central part of China. In this region, changes in precipitation exhibit a more pronounced negative trend, particularly during the winter tillering period (Zhai et al 2005). Consequently, in central China, moisture stress, rather than temperature, may be the primary factor limiting wheat production. During the overwintering stage, the correlation between the sliding trend of temperature-related variables and that of the winter wheat yield is strongest in Region I, which represents southeastern China. This can be attributed to the temperate climates , characterized by higher local heat stress, ample moisture, more frequent wintery precipitation, and the high climate sensitivity in this region . This may result in the strongest negative impacts on the winter wheat yield during the overwintering stage in southeastern China from winter warming and hot extremes and positive impacts from cold extremes that are always accompanied by wintery precipitation.
We have also primarily examined the abovementioned relationships respectively in wet and dry winters because of the substantial influence of precipitation on grain yield (Falloon and Betts 2010, Ray et al 2015, Zhu et al 2018. As shown in the Supplementary Information (Figures S8-S11), we have observed more prominent negative correlations between the IMFs of the T _ , 2m var EHD, and ECD in wet winters at the multidecadal timescale. In contrast, T _ 2m var and EHD in dry winters display significant positive correlations with winter wheat yield at the multidecadal timescale. Therefore, one may expect that the adverse impact of temperature variations and extremes on the winter wheat yield seems to be amplified by the more abundant moisture, which is reported to be increasing significantly with global warming (Ren et al 2015.

Conclusions
This study investigated the impact of temperature-related conditions (the average winter temperature (T 2m ), its variance (T _ 2m var ), EHD and ECD), on China's winter wheat yield, using observational data in 1948-2018 and linear trend analysis, EEMD method, and sliding trend analysis. The relationship is revealed not only at the China's national but at regional scale and not only for the entire winter growth period of winter wheat but also for different growth stages.
Results showed a significant linearly increasing trend in the China's national total winter wheat yield and T m 2 since 1949, while after 1985, T _ , m var 2 EHD and ECD also exhibited increasing trends. EEMD analysis yields that the China's national total winter wheat yield tends to vary in-phase with the T m 2 but out-of-phase with T _ , m var 2 EHD and ECD on time scale longer than 20 years. Nevertheless, these correspondences in long-term changes did not necessarily imply causality between wheat yields and temperature conditions, as they may vary for different reasons. The sliding trends were further derived to gain a deeper understanding of the changing rates of variables. An investigation of the relationship between the changing rates of winter wheat yield and temperaturerelated variables is found to be useful for understanding how China's total wheat yield relates to various temperature conditions, as the changing rates of winter wheat are expected to be more regulated by climatic factors than the persistent socio-economic and technological development.
Further investigations conducted from a wheat growth stage-based and region-based perspective reveal that, in the majority of cases, the temperature impact on winter wheat yield demonstrates regional consistency with significant differences observed. Across the entire growth period, there exists a negative effect on the winter wheat yield attributable to greater temperature variability in all regions of China, which is predominantly observed in southeastern China. This phenomenon can be ascribed to the heightened levels of pre-existing heat stress experienced in the southern regions .
At the overwintering stage, the sliding trends of T , 2m T _ 2m var and EHD were found to be negatively correlated with winter wheat yield across decadal to multi-decadal scales, while the sliding trend of ECD showed a positive correlation with that of winter wheat yield at the interdecadal scale. This finding suggests that during the overwintering stage, characterized by the winter wheat's relatively strong cold resistance, a prolonged period of low temperature and multiple occurrences of extreme cold events accompanied by wintery precipitation can have a positive impact on winter wheat yield. This positive impact may be attributed to several factors, such as preventing premature transition to more cold-sensitive growth stages (Kosová et al 2008), facilitating the accumulation of dry matter in wheat, and enhancing resistance to pests and diseases (Guo and Huang 2009, Gaudet et al 2011, Vanková et al 2014, Skendžić et al 2023. In contrast, warm temperatures and an increased frequency of extreme heat events tend to have negative impacts on winter wheat yield. These negative impacts are primarily manifested in the delayed emergence of seedlings and a reduction in the cold resistance of winter wheat Zhai 1998, Salazar-Gutierrez et al 2013). Moreover, during the overwintering stage, the correlation between temperature-related variables and winter wheat yield is strongest in the southeastern region of China. This observation can be attributed to the fact that southeastern China (Region III) falls within the temperate climates , characterized by higher local heat stress and greater winter precipitation. Additionally, this region exhibits higher climate sensitivity . Thus, this may lead to the most pronounced negative impacts from winter warming and hot extremes, as well as positive impacts from cold extremes, which are consistently accompanied by wintery precipitation. At the tillering stage, when considering decadal to multi-decadal scales, the analysis of sliding trends reveals a positive relationship between the sliding trends of winter wheat yield and the sliding trends of T .
2m Conversely, negative associations are observed with the remaining three temperature-related variables. Central China (Region II) displays the weakest correlation among the regions, possibly due to a significant downward trend in precipitation variability (Zhai et al 2005), whichparticularly affects the tillering stage, which is in the winter season, resulting in a relatively minor contribution of temperature impact on winter wheat yield during this specific period. During the reviving growth stage, however, we hardly found a significant relationship between the changing rate of winter wheat yield and that of temperature-related variables.
Indeed, it is important to acknowledge that there are multiple factors, aside from temperature, that can influence China's winter wheat yield (e.g., Demotes-Mainard et al 1995, Abbate et al 1997, Cromey et al 1998, Schillinger 2011, Chen et al 2020. Relying solely on a statistical analysis of the available data may not provide a rigorous enough assessment of the relationship between temperature and winter wheat yield. It is crucial to consider other relevant factors and conduct comprehensive studies to obtain a more accurate understanding of the complex dynamics impacting winter wheat yield in China. Nonetheless, our study has effectively examined the relationship between various temperature conditions and their changing rates in winter, in relation to winter wheat yield at different growth stages and in different regions of China. By considering multiple perspectives and maximizing the utilization of available data, we have provided valuable observational insights and constraints for assessing and enhancing the representation of climatic impacts on winter wheat yield in climate models under the global warming scenario. Through unraveling the intricate connections between temperature conditions and winter wheat yield, our study offers invaluable insights into the underlying mechanisms and processes governing these relationships. This understanding can inform the development of more sophisticated climate models, encompassing enhanced representations of temperature impacts on winter wheat yield. These findings are particularly significant in enhancing the accuracy of future projections and fostering a deeper comprehension of the potential implications of climate change on winter wheat yield.