Responses of Winter Wheat Yield to Drought in the North China Plain: Spatial–Temporal Patterns and Climatic Drivers

Abstract

Understanding the winter wheat yield responses to drought are the keys to minimizing drought-related winter wheat yield losses under climate change. The research goal of our study is to explore the response patterns of winter wheat yield to drought in the North China Plain (NCP) and then further to study which climatic factors drive the response patterns. For this purpose, winter wheat yield was simulated by the Environmental Policy Integrated Climate (EPIC) crop model. Drought was quantified by standardized precipitation evapotranspiration index (SPEI), and the contributions of the various climatic factors were evaluated using predictive discriminant analysis (PDA) method. The results showed that the responses of winter wheat yield to different time-scale droughts have obvious spatial differences from the north part to the south part in the NCP. Winter wheat yield is more sensitive to the medium (6–9 months) and long (9–12 months) time-scale droughts that occurred in the key growth periods (April and May). The different response patterns of winter wheat yield to the different time-scale droughts are mainly controlled by temperature and water balance (precipitation minus potential evapotranspiration) in winter in the NCP. Compared with the water balance, temperature plays a more important role in driving the response pattern characteristics. These findings can provide a reference on how to reduce drought influences on winter wheat yield in the NCP.

1. Introduction

Drought usually leads to serious agricultural damage and the negative effects of drought cannot be ignored. It is considered as the main meteorological disaster influencing crop production and food security in the world [1,2]. The agriculture of China is likely to be faced with higher drought risk because of continuous climate change [3]. Based on the record of the Chinese Academy of Agricultural Sciences (CAAS), the mean annual crop production losses in China caused by drought were up to 75.7 billion yuan from 1988 to 2004. The grain losses are up to 10 billion kg every year because of drought [4]. Understanding the influence of drought on agriculture is central to minimizing drought-related yield losses and can help farmers reduce the adverse effects of drought on agriculture [5].

As a complex natural disaster, it is not easy to establish a unitary multidisciplinary definition of drought [6,7,8]. For the purpose of reflecting the spatial–temporal distribution characteristics of drought, many drought indexes have been put forward, such as the standardized precipitation index (SPI), Palmer drought severity index (PDSI), and the standardized precipitation evapotranspiration index (SPEI). The SPEI has been widely used in drought monitoring [9,10,11]. Compared with the SPI [12], the SPEI is especially suitable for evaluating the drought influences against the backdrop of global warming [13], since SPEI takes into account the influences of the temperature. PDSI has also been widely used in drought monitoring and assessment, but the major limitation of PDSI is its incomparable parameters in different regions [14]. It should be noted that each drought index has its strengths and weaknesses. However, by comparing the performance of the above three drought indices, it also has been proven that the SPEI performed better than SPI and PDSI in estimating the drought influences on crop production in the NCP [15,16]. Additionally, by studying the drought effect on winter wheat yield of the region, Liu et al. [17] pointed out that the SPEI could explain the extensive winter wheat yield fluctuations of this region. Therefore, in our study, SPEI was selected as the drought indicator to evaluate the different response patterns of winter wheat yield to drought.

Due to the significant impact of drought on crop yield, a series of studies on the crop yield responses to drought have been carried out at different temporal and spatial scales. At the global scale, the nonlinear responses between crop yield and drought severity have been found by analyzing the responses of wheat, corn, rice, and soybeans to drought [18]. For maize, soybeans, and wheat, drought has significantly reduced their yields globally [19]. By analyzing the sensitivity of 10 main crops to drought in the United States, Lu J. et al. (2020) [20] pointed out that drought stress that occurred in the reproductive stage will severely reduce crop yield. Based on the field experiment on maize, the increased sensitivity to drought stress of maize yield has been found in the central United States [21]. Using the grid crop models to quantify the contributions of various climatic drivers to past yield variability in maize and winter wheat, Webber H. et al. (2018) found that drought stress persists as the main driver of losses for the both crops [22]. Based on the APSIM crop model simulation, the reduced rainfall was considered as one of the reasons of wheat yield decline in Australia [23]. By the empirical relationships between drought intensity and yield fluctuation which were identified by the Bayesian hierarchical model, Chen H. et al. (2018) pointed out that drought significantly reduced grain yields in 28 of 31 provinces in China and obvious spatial variability in drought sensitivity exists [24]. In the NCP, Yu, H. et al. (2018) studied the drought influences on winter wheat at different growing periods in Eastern China and found that ensuring the adequate irrigation is very important during the flowering and filling stages to guarantee normal winter wheat yield [25]. By investigating the drought effect on winter wheat yields of the region, Liu X. et al. (2018) pointed out that the SPEI could explain the extensive winter wheat yield fluctuations of this region [17].

Climate factors play an import part in driving the crop yield variations. Numerous studies have explored how climate factors drive the crop yield variability. Based on the detailed crop statistics time series, Ray D.K. et al. (2015) pointed out that climate variability led to about one third of the observed crop yield variability, including maize, rice, wheat, and soybean [26]. By crop model simulation and statistical regression methods, Qiao J. et al. (2017) [27] found that precipitation contributed more than other climatic factors in driving the crop yield variations at the semiarid region. To understand the drivers of crop production in sub-Saharan Africa, Hoffman, A.L. et al. (2017) [28] explored the relationship between crop yields and climate data with random forest, and they found that though climate variables played a comparatively small role compared technological advances, crop yields exhibited distinct responses to maximum temperature, accumulated precipitation, and vapor pressure deficit. The spatial differences in the contribution of different climatic drivers to crop yield variability also have been explored. Ceglar A. et al. (2016) [29] found the meteorological factors that dominate the variations in winter wheat and corn yield are different in different regions of France.

The above research conclusions can improve our understanding on the response patterns of crop yield to drought and how climatic factors influence crop yields. However, as for the drivers leading to the different responses of crop yield to drought, current studies are mainly carried out from the perspective of crop physiology to explain the reasons causing the different responses of winter wheat yield to drought. The differences of the winter wheat varieties are the internal cause for the different responses of winter wheat to drought. The physiological responses (such as stomatal regulation ability, osmotic adjustment capability) to drought is different among the different varieties [30]. Climatic factors are considered as the important external factors leading to the different response patterns of crop yield to drought. However, there are only few studies that have focused on which climatic factors contribute more to the different response patterns of crop yield to drought. At the global scale, Leng et al. (2019) [18] found that temperature plays an important role in determining the impact of drought by sensitivity analysis. In the United States, Pena-Gallardo et al. [31] found that the different response patterns of crop yield to drought were mainly controlled by the average climatic conditions, especially by the water availability. As mentioned above, in the NCP, previous studies mainly focused on the relationship between drought index and crop productions. Some studies explore the drivers leading to the different responses only from the perspective of vegetation physiology [30]. However, in the NCP, our understanding on which climatic factors drive the different response patterns of winter wheat yield to drought is very limited. In order to minimize drought-related winter wheat yield losses, we need to further study the role of different climatic factors in driving winter wheat drought response.

The NCP is an important winter wheat production base in China. Drought condition of the NCP has worsened in the past several decades [32]. Hence, studying the response patterns of winter wheat yield to drought, especially exploring the climatic factors causing the different response patterns, are significant for reducing the drought-related winter wheat yield losses. The main purposes of our research are (i) to identify the possible spatial patterns of winter wheat yield responses to different time-scale droughts and (ii) to explore the climatic characteristics that determine these patterns.

2. Materials and Methods

2.1. Study Region

The North China Plain (NCP, 113° E~123° E, 32° N~42° N) (Figure 1) is the main winter wheat production base and supplies 50% of China’s winter wheat production. The rainfall during the winter wheat growing season is about 100–350 mm. According to the rainfall of the winter wheat growing season, we divided the NCP into three parts: (I) the north parts, (II) the central parts, and (III) the south parts. Significant seasonal precipitation anomalies caused by the monsoon climate can be observed in this region. As a result, severe drought often occurs in the area, and drought has become one of the most prominent factors restricting the growth of winter wheat in the region.

2.2. Data

The main dataset applied in this study consists of meteorological data, observed winter wheat production records, and soil data. (1) There are 47 stations (including 31 meteorological stations and 16 agrometeorological stations) in this region that were chosen for data collection. Daily meteorological data from 1980 to 2013 were obtained from the China Meteorological Data Sharing Service System (http://data.cma.cn/), which includes the temperature (°C), precipitation (mm), relative humidity (%), sunshine duration (h), and daily average wind speed (m/s). We calculated the solar radiation (MJ/m²) using the sunshine duration by the Ångström function, and the potential evapotranspiration (PET) (mm) was estimated according to the Penman–Monteith equation [33]. (2) The soil data was collected from the Food and Agriculture Organization of the United Nations (FAO), it includes the number of soil layers and the properties for every layer. (3) The observed winter wheat yield at 16 agrometeorological stations for the crop model calibration was obtained from the National Climate Center of China.

2.3. Methods

The methodological framework of our study is shown in Figure 2. The main flowchart of our study includes (1) collect daily climate data, basic geographical data and agrometeorological data. (2) Calculate the different time-scale SPEI as the drought index. (3) Simulate the winter wheat yield by the calibrated EPIC crop model. (4) Study the response patterns of winter wheat yield to drought using the Pearson correlation analysis and principle component analysis (PCA) method. (5) Explore the climatic drivers by the predictive discriminant analysis (PDA) method.

2.3.1. Standardized Precipitation Evapotranspiration Index (SPEI)

The PET which is estimated by the Penman–Monteith equation and the precipitation were used to calculate the SPEI. SPEI is not only sensitive to the evaporation changes but also can describe the multiscale drought character. Details of the approach on how to compute the drought index have been described by Vicente-Serrano et al. [13]. In our research, we calculated the 1-month to 12-month time-scale SPEI from 1980 to 2013 in the NCP. The classifications of different levels of drought and moist by SPEI are shown in

Table 1. Drought/moisture level based on SPEI.

Drought/Moisture Level	SPEI Values
Mild moisture	SPEI ≥ 2.0
Moderate moisture	1.5 < SPEI <2.0
Severe moisture	1.0 < SPEI ≤ 1,5
Extreme moisture	0.5 < SPEI ≤ 1.0
Normal	−0.5 < SPEI ≤ 0.5
Mild drought	−1.0 < SPEI < −0.5
Moderate drought	−1.5 < SPEI ≤ −1.0
Severe drought	−2.0 < SPEI ≤ −1.5
Extreme drought	SPEI ≤ −2.0

.

2.3.2. Environmental Policy Integrated Climate (EPIC) Model and its Localization

The EPIC crop model has been widely applied in the research on how drought affects crop yield due to its advantages in simulating crop growth processes; it has been applied in studies in the NCP for different topics such as irrigation management [34], potential winter wheat yield simulation [35], and crop drought risk assessments [36]. To simulate the winter wheat yield, the input data mainly consists of meteorological data, soil data, and field management data. The simulated principles and processes of the crop growth model are shown in Figure 3. Harvest index is used to convert the above-ground biomass to crop yield in the crop model. The details of the crop model can be found in Wang et al. [37].

Crop model localization helps to determine winter wheat variety parameters in the different regions of the NCP. The cultivars of winter wheat may change during the study periods. To remove the effects of changes in wheat varieties, in our research, by crop model calibration, we would obtain crop parameters that can represent the average condition of winter wheat varieties for many years in the NCP. This set of crop parameters remains unchanged throughout the simulation process, so that we can eliminate the impact of variety differences over the years. According to previous study [38,39], the following eight crop parameters (Table S1) were chosen to calibrated: (1) biomass–energy ratio (WA), (2) harvest index (HI), (3) potential heat unit (PHU), (4) fraction of growing season when leaf area declines (DLAI), (5) first point on optimal leaf area development curve (DLAP1), (6) second point on optimal leaf area development curve (DLAP2), (7) maximum potential leaf area index (DMLA) (8) leaf area index decline parameters (RLAD), which are most sensitive parameters for winter wheat yield simulation.

In this study, 16 agrometeorological stations (Figure 1) were selected to calibrate and verify the crop model based on the winter wheat plant region and the available data. A global optimization algorithm named Shuffled Complex Evolution algorithm—University of Arizona (SCE-UA) [40] was used to verify the EPIC model at these stations. Compared with traditional “trial-and-error” method, the SCE-UA is a global optimization method. There are about 180 yield records of all the stations, the observation yield records from 1999 to 2008 were used for model calibration and the observation yield records from 2009 to 2011 were used for model validation. The normalized root mean square error (N_RMSE) and Pearson correlation coefficients were used to measure the precision of the model localization.

$$\mathrm{RMSE}=\sqrt{{{\displaystyle {\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{Yield}}_{\mathrm{si}}{}_{}^{}-{\mathrm{Yield}}_{\mathrm{oi}}\right)}}^2}$$

(1)

$$\mathrm{Yiel}{\mathrm{d}}_{\mathrm{o}\_\mathrm{mean}}=\frac{1}{n}{\displaystyle {\sum }_{i=1}^n\mathrm{Yiel}{\mathrm{d}}_{\mathrm{oi}}}$$

(2)

$$N\_\mathrm{RMSE}=\frac{\mathrm{RMSE}}{\mathrm{Yield}{\mathrm{d}}_{\mathrm{o}\_\mathrm{mean}}}$$

(3)

where n is the number of samples, Yield_si is the simulated winter wheat yield, ${\mathrm{Yield}}_{\mathrm{oi}}$ is the observed winter wheat yield and Yield_{o_mean} is the average observed yield. N_RMSE could express the differences between simulated productions and observed productions.

Irrigation management has influences on winter wheat in the NCP. However, it is difficult to get enough irrigation information. In our study, the averaged sowing date (Figure S1a) was used in the EPIC model, because the observed sowing date were only delayed on averaged by 1.5 days per decade in the NCP [41]. In the same method, we calculated the averaged wintering date (Figure S1b), the averaged jointing date (Figure S1c), and the averaged filling date (Figure S1d) as the reference of the irrigation date. The irrigation schedule for NCP was set up based on our field investigations and previous research conclusions [42,43,44]. In the north part of the NCP, we irrigated three times at wintering stage, jointing stage, and filling stage; in the central part of the region, we irrigated twice at jointing stage and filling stage; in the south part of the region, we only irrigated one time in the jointing stage (Table S2).

2.3.3. Statistical Methods

Three kinds of statistical methods were used in the study. The Pearson correlation analysis was used to evaluate the drought influence on winter wheat yield. The principal component analysis (PCA) method was used to identify the responses of winter wheat yield to drought. Additionally, the predictive discriminant analysis (PDA) was chosen to explore the driving climatic factors of winter wheat yield responses to different time-scale droughts.

(1)

Pearson correlation analysis

Drought influences on the winter wheat yield were assessed by Pearson correlation analysis. The correlation coefficients were computed between the winter wheat yield and the 1-month to 12-month time-scale SPEI series at each station (including meteorological stations and agrometeorological stations) in the winter wheat growing season (from October of the year to June of the following year). Thus, for each station, we obtained 108 correlation coefficients (9 months × 12 time-scales) (Figure 4).

We get the maximum correlation coefficients at each station as follows:

$${\mathrm{R}}_{\mathrm{i},\mathrm{j}}=\mathrm{cor}\left(\mathrm{Yield},\mathrm{SPE}{\mathrm{I}}_{\mathrm{i},\mathrm{j}}\right)\hspace{1em}\mathrm{i}\in \mathrm{w}\mathrm{int}\mathrm{erw}\mathrm{heatgrowingseason},1\le \mathrm{j}\le 12$$

(4)

$$\mathrm{w}\mathrm{int}\mathrm{erw}\mathrm{heatgrowingseason}=\{10,11,12,1,2,3,4,5,6\}$$

(5)

$${\mathrm{R}}_{\max }=\max ({\mathrm{R}}_{\mathrm{i},\mathrm{j}})$$

(6)

where cor is the Pearson correlation analysis, i is the month which belongs to the winter wheat growing season, j represents the time-scale of drought, ranging from 1 to 12 months; Yield is the winter wheat yield simulation series at one station from 1981 to 2013; SPEI_i,j is the ith month drought index with time-scale of j; R_i,j is the Pearson correlation of Yield and SPEI_i,j; R_max is the maximum correlation coefficients at each station. As the simulation length is 33 years, the values of 0.35 are responses to 5% significant levels of those correlation coefficients.

(2)

The principal component analysis (PCA) in spatial model

The principal component analysis (PCA) in spatial model [45] was chosen to identify the response patterns of winter wheat yield to different time-scale droughts. In our study, 47 stations were chosen to simulate the winter wheat yield, and 108 correlation coefficients were obtained at each station. Therefore, we can get a correlation matrix (47 rows × 108 columns). The PCAs decompose the matrix into two parts: loading matrix and score matrix (Figure 5).

The principal component equals the one special column of the loading matrix multiplied by the corresponding row of the score matrix (Figure 5). Each principal component has different variance. The larger the variance is, the more representative the principal component is. By comparing the variance of each principal component, several representative principal components were selected, which own stronger ability to characterize the different responses of winter wheat yield to drought. The classifications of the different response patterns were according to the maximum principal component loading rules [46]. Among different stations, the closer the principal component loadings are, the more similar the response patterns of winter wheat yield to drought are. In other words, the principal component loading spatial map could help us to identify stations with similar response patterns of winter wheat yield to drought.

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(3)

Predictive discriminant analysis

Predictive discriminant analysis (PDA) is commonly used to explain the value of a dependent categorical variable based on its relationship to one or more predictors. Given a set of independent variables, PDA attempts to identify linear combinations of those variables that best separate the groups of cases of the dependent variable. According to prior studies [31,46], the PDA method was chosen to study the driving factors of winter wheat yield to drought in the NCP. The basic problem solved by the predictive discriminant analysis (PDA) is to evaluate the relative importance of multiple independent variables to the dependent variables [47]. In this study, the PDA method was used to explore the driving climatic factors of winter wheat yield responses to different time-scale droughts. A set of climatic variables including precipitation, maximum temperature, minimum temperature, mean temperature, potential evapotranspiration, water balance (precipitation minus potential evapotranspiration) were considered as the predictive variables (independent variables), and the winter wheat yield response patterns to drought were considered as the grouping variables (dependent variables). We can get several predictive discriminate functions (Equation (7)) with different discriminate ability [48] after the PDA method. The first function which is able to separate the different response patterns as much as possible was defined automatically in the PDA, then is the second function and further functions until the number of functions reaches the maximum number according to the number of response patterns. These functions were a multiple linear combination of climatic variables which can best separate the response patterns of winter wheat yield to drought.

$$\mathrm{Func}\left(\mathrm{clim} \mathrm{ate} \mathrm{factors}\right)={\mathrm{w}}_1\times \mathrm{c}{\mathrm{f}}_1+{\mathrm{w}}_2\times \mathrm{c}{\mathrm{f}}_2+\dots +{\mathrm{w}}_{\mathrm{i}}\times \mathrm{c}{\mathrm{f}}_{\mathrm{i}}$$

(7)

where cf_i represents the different climate factors, W_i is the coefficients of one specific climatic factor. If the absolute value of W₁ is greater the absolute value of W₂, it means cf₁ has greater effect than cf₂ in driving the response patterns of winter wheat yield to drought in the NCP.

3. Results

3.1. EPIC Crop Model Verification

EPIC crop model verification is the basis for the application of the model in the NCP. The cultivar parameters of the EPIC crop model were calibrated by the SCE-UA method at 16 agrometeorological stations. At each station, Firstly, the crop yield records from 1999 to 2008 were used for EPIC model calibration, the correlation coefficient between the observed and simulated winter wheat yield was 0.86 (p < 0.01), and the N_RMSE was 9.8% (Figure 6a). Secondly, the crop yield records from 2009 to 2011 were used for EPIC model validation, the correlation coefficient was 0.65 (p < 0.01), and the N_RMSE was 10.9% (Figure 6b). The N_RMSE is within the acceptable range [49], which indicated that the EPIC model after calibration was suitable for simulating winter wheat yield in the NCP [50].

3.2. Diverse and General Spatial–Temporal Patterns of Winter Wheat Yield Responses to Drought

3.2.1. Diverse Responses of Winter Wheat Yield to Drought

For each month of all 47 stations, we obtained the time-scales of SPEI (Figure 7a) and the correlation coefficients (Figure 7b), when the winter wheat yield and SPEI correlation coefficients are the highest. The mean value of the time-scales of SPEI was usually not less than 6 months (Figure 7a). Additionally, drought occurring in April and May usually have higher correlation coefficients with winter wheat yield compared with those of droughts in other months (Figure 7b), which indicates that drought occurring in April and May would have a more serious influence on winter wheat. In summary, the winter wheat yield is usually more sensitive to the medium (6–9 months) time-scale drought and long (9–12 months) time-scale drought during the critical period of winter wheat growth, such as April and May.

When the correlation coefficient reaches the highest between winter wheat yield and SPEI, we obtained the best time-scales of SPEI and the months at each station. The best time-scales of SPEI varied obviously from the north part to the south part of the NCP (Figure 8a). In the north part of the region, the long time-scale drought (9–12 months) has a more significant impact on winter wheat yield. However, in the central part of the region, winter wheat yield is more susceptible to the medium time-scale drought (6–9 months). For the south part of the region, winter wheat yield tends to be affected by short time-scale drought (1–3 months), though the influence was not significant (p > 0.05). This may be because the rainfall in the southern part of the NCP is relatively abundant and the potential evapotranspiration is smaller compared with those in the northern and central parts of the NCP. Overall, medium and long time-scale drought occurring in the critical period of winter wheat growth (heading stages, flowering stages, fill stages during April and May) has more obvious influences on the winter wheat yield (Figure 8b,c) in the NCP.

3.2.2. General Spatial Patterns of the Winter Wheat Yield Responses to Drought

The PCAs method was applied for generalizing the general spatial response patterns of winter wheat yield to different time-scale droughts. Different principal component represents the different response patterns. The larger the variance of one principal component is, the more representative of the principal component is. As Figure 9 shows, the variance of the first two principal components (the principal component 1 and the principal component 2) occupy approximately 90% of the total variance. This means a clear response pattern of the relationship between winter wheat productions and the different time-scale droughts can be summarized by the first two principal components. Therefore, the first two principal components were selected for further analysis of the characteristics and spatial distributions of these two main response patterns.

PC1 presents strong winter wheat yield-SPEI correlations at long time-scales drought (9–12 months), especially from March to May (Figure 10b). The stations that show significant responses to long time-scale drought (PC1) are mainly situated at the north region of the NCP. Conversely, stations located in the south region show a negative relationship between winter wheat yield and SPEI (Figure 10a). Additionally, higher correlations at medium time-scale (6–9 months) of SPEI during May (Figure 10d) were found at the winter wheat yield responses to drought summarized by PC2. PC2 did not exhibit significant correlations between different time-scale of SPEI and winter wheat yield in the NCP (Figure 10c). Overall, the winter wheat planted in more arid stations showed a more significant response to the SPEI. Conversely, winter wheat planted in a relatively humid environment usually show a lower sensitivity to the variability of SPEI (Figure S2). The findings were consistent with the conclusion that crop yield responses to drought are nonlinear [11,51].

To study the climatic driving factors, we used the maximum loading rule to classify the different types of winter wheat yield responses to the different time-scale droughts (

Table 2. Percentages of the first two principal components (PC1 and PC2) summarizing the winter wheat yield responses to the SPEI.

Group (Effect)	PC1		PC2
	PC1+	PC1−	PC2+	PC2−
Percentage	58%	14%	19%	9%

). Winter wheat with responses to long time-scale drought represented 72% of the analyzed stations, but 58% showed a positive response (positive loadings) of winter wheat yield to drought, while the remaining 14% showed a negative response (negative loadings) to drought. This means we were able to obtain two different groups of winter wheat according to PC1, which, respectively, described positive (+) or negative (−) responses of winter wheat yield to long time-scale drought. Adopting the same process to the second principal component, we found that the stations with responses to medium time-scale drought (PC2) represented 28% (19% positive loadings and 9% negative loadings).

3.3. Factors Explaining the Different Responses of Winter Wheat Yield to Drought

To consider the possible influence of climate factors on the responses of winter wheat yield to different time-scale droughts, we analyzed the magnitudes of the mean air temperature, maximum air temperature, minimum air temperature, precipitation, PET, water balance (precipitation minus PET), relative humidity, wind speed, and sun radiation during the winter wheat growth season.

The stations presenting a negative response to long time-scale drought (PC1−) are generally situated in the south region of the NCP, in which the climate conditions are more humid and warmer than the winter wheat stations that showed a positive response to long time-scale drought (PC1+) (Figure 11). Thus, the negative relationship between winter wheat yield and drought are probably caused by higher temperature and precipitation conditions. The main climatic factors that influence the positive responses to the medium time-scale drought (PC2+) and the negative responses to the medium time-scale drought (PC2−) are complex and include wind speed, relative humidity, and sun radiation in different seasons (Figures S3–S6). Overall, winter wheat stations represented by PC2+ are usually with higher relative humidity, wind speed, and sun radiation than those represented by PC2− (Figure 11). When the winter wheat showed positive responses to drought, the winter wheat plant region with a positive response to long time-scale drought (PC1+) were usually much drier than the region with a positive response to medium time-scale drought (PC2+). However, in terms of winter wheat corresponding to negative responses to drought, the region where winter wheat showed higher correlations with long time-scale drought are usually with a higher water balance and higher temperature compared with the areas where winter wheat was more sensitive to medium time-scale drought (Figure 11).

The PDA function quantified the relative importance of the various climatic factors for driving the winter wheat yield response patterns to drought (

Table 3. Structure matrix of the three PDA functions for winter wheat (the explained variance by each function is indicated in parentheses; the greater the variance is, the stronger the explanatory power of the discriminant function owns.). The correlation values computed for every environmental factor are displayed as well.

Variables	PDA Functions (Percentage of Variance)
	PDA1 (62.2%)	PDA2 (30%)	PDA3 (7.8%)
Pre(winter)	−0.372 *	−0.126	−0.008
Latitude	0.366 *	0.109	−0.044
Tmean (winter)	−0.334 *	−0.064	−0.029
Water balance (winter)	−0.330 *	−0.220	0.020
Tmean (autumn)	−0.324 *	0.016	−0.083
Tmax(autumn)	−0.324 *	−0.069	−0.128
Water balance (spring)	−0.322 *	−0.234	0.277
Rhu (winter)	−0.317 *	−0.045	0.061
Pre (spring)	−0.315 *	−0.187	0.046
Tmin (winter)	−0.315 *	−0.028	−0.025
Tmax (winter)	−0.311 *	−0.116	−0.039
Tmin (annual)	−0.311 *	−0.014	−0.151
Rhu (annual)	−0.304 *	−0.093	0.242
Tmean (annual)	−0.300 *	−0.057	−0.232
Pre (autumn)	−0.299 *	−0.208	0.092
Water balance (autumn)	−0.294 *	−0.260	0.262
Rhu (spring)	−0.293 *	−0.099	0.233
Pre (annual)	−0.284 *	−0.177	0.085
Tmin (autumn)	−0.276 *	0.035	−0.062
Rhu (autumn)	−0.243 *	−0.124	0.182
Rs (summer)	0.228 *	0.197	−0.194
Pre (summer)	−0.175 *	−0.139	0.102
Water balance (autumn)	−0.254	−0.364 *	0.145
Rs (autumn)	0.240	0.267 *	−0.009
Rs (annual)	0.143	0.227 *	−0.009
PET (autumn)	−0.032	0.223 *	−0.078
Wind (summer)	−0.021	0.219 *	0.027
Wind (spring)	0.054	0.216 *	0.021
Wind (annual)	0.014	0.202 *	0.055
Wind (autumn)	0.010	0.201 *	0.054
Rs (autumn)	0.044	0.199 *	0.140
Wind (winter)	0.016	0.167 *	0.110
Rs (winter)	−0.067	0.163 *	0.123
PET (winter)	−0.084	0.103 *	−0.034
PET (summer)	0.190	0.205	−0.608 *
PET (spring)	0.247	0.230	−0.488 *
PET (annual)	0.142	0.283	−0.487 *
Tmean (summer)	−0.116	−0.044	−0.433 *
Rhu (summer)	−0.211	−0.064	0.416 *
Tmin (summer)	−0.271	−0.023	−0.381 *
Tmax (summer)	−0.024	−0.057	−0.366 *
Tmean (spring)	−0.151	−0.076	−0.320 *
Tmax (spring)	−0.063	−0.081	−0.312 *
Tmin (spring)	−0.260	−0.044	−0.285 *
Water balance (summer)	−0.203	−0.177	0.263 *
Tmax (annual)	−0.188	−0.097	−0.252 *
Altitude	0.002	0.010	0.199 *
Longitude	0.010	0.107	0.146 *

The environmental factors are marked with asterisks (*) while p-value < 0.05. “Pre” is “precipitation”; “Tmean” is the “mean temperature”; “Tmax” is “maximum temperature”, “Rhu” is “relative humidity”, “PET” is “potential evapotranspiration”, “Water balance” is “precipitation minus potential evapotranspiration”, “Wind” is “mean wind speed”, “Rs” is “sun radiation”.

). The first PDA function (PDA1) accounts for 62.2% of the total variance and allows the four patterns (PC1+, PC2+, PC1−, PC2−) of winter wheat yield responses to the different time-scale droughts to be differentiated. According to the coefficient of each climatic factor (Table 3), we can find that the PDA1 mainly represents the latitude, winter climatic conditions (including mean temperature, precipitation, and water balance), and mean temperature and max temperature in autumn at each station. In other words, the PDA1 showed that the winter climatic conditions and temperature have an important impact on winter wheat yield response to drought. The second PDA function (PDA2) could explain 30% of the variance and shows significant correlations with the water balance, especially the autumn water balance. The PDA2 revealed that the water balance also plays an important part in influencing the response characteristics. The third PDA function (PDA3, 7.8% of variance) mainly represents the influence of PET on the winter wheat yield responses to drought. In summary, the above three PDA functions highlight the importance of the different climatic factors to discriminate the different patterns of winter wheat yield responses to drought. Additionally, the climate conditions in winter play a more important part in discriminating the different patterns of winter wheat yield responses to drought. Additionally, compared with the water balance, the temperature plays a more important role in driving the response pattern characteristics.

PDA1 discriminates between winter wheat with a positive response to long time-scale drought (PC1+) and a negative response to long time-scale drought (PC1−) well (Figure 12). This means that whether the winter wheat yield show positive responses to long time-scale drought (PC1+) or negative responses to long time-scale drought (PC1−) is mainly controlled by latitude and winter climate conditions (including mean temperature, precipitation, and water balance). This conclusion also applies to the positive response to medium time-scale drought (PC2+) and the negative response to medium time-scale drought (PC2−). It also can be found that the centroids of PC1+ (winter wheat yield with positive response to long time-scale drought) and PC2− (winter wheat yield with negative response to medium time-scale drought) are close to each other, which means that the different responses to drought characterized by PC1+ and PC2− are not mainly controlled by the above climate conditions. However, PDA2, mainly representing water balance, was able to distinguish between wheat with PC1+ and PC2−, which means the differences between the positive response to long time-scale drought (PC1+) and the negative response to medium time-scale drought (PC2−) are more susceptible to water balance. Though PDA3 only accounts for 7.8% of the total variance, it can be considered to represent the impacts of PET, especially the summer PET and spring PET (Table 3). PDA3 can clearly differentiate between winter wheat that has a positive response to medium time-scale drought (PC2+, humid but with low PET) and winter wheat that has a negative response to long time-scale drought (PC1−, humid with high PET).

4. Discussion

The results of our study clearly showed that the correlation between the winter wheat production and drought is spatially variable and relied on the drought time scales quantified by the SPEI. However, there is still a uniform pattern in the responses of winter wheat yield to drought: the medium time-scale (6–9 months) drought and long time-scale (9–12 months) drought occurring in the key growth periods (April and May) usually have the greatest impact on the yield in the north and central region of the NCP, though winter wheat planted in the south part of the NCP were more sensitive to the short time-scale (1–3 months) drought. As for the other question, which climatic factors lead to this kind of response pattern, we found climate conditions in winter play a more important part in discriminating the different patterns of winter wheat yield responses to drought. Additionally, compared with the water balance, the temperature plays a more important role in driving the response pattern characteristics of winter wheat yield to drought.

4.1. The Mechanisms of the Different Responses of Winter Wheat Yields to Drought

Winter wheat yields are easily influenced by severe droughts that occur in the key growth stages from April to May compared with other stages, just as Xu et al. (2018) has found [52]. In addition, a series of studies which aimed at different crop types and were carried out in different regions all indicated that the crop yields were more easily influenced by drought that occurred at the critical growth stages [11,31,53]. There are several reasons leading to the phenomenon. Firstly, the different growth stages own different resistances to drought [54] due to the different physiological characteristics and the different field management [55] of each growth period. When drought occurred in the earlier stage, winter wheat may have enough time to remedy itself with a positive irrigation management and the influence of drought on winter wheat will be alleviated [52]. Secondly, droughts that occurred at different growth stages have different effects on yield formation. During the flowering stage, drought mainly reduced the success rate of pollination and increased the floret death and which leads to a reduction of spikes number. Drought that occurred at the wheat filling periods affects the transfer of substances from other organs to wheat ears, resulting a thousand-grain weight reduction [56].

Different climatic conditions from the north region to the south region of the NCP caused the different sensitivity of winter wheat yield to the time-scale of drought. In the relative dry region (including the north region and the central region of the NCP), winter is the key season for the soil moisture supply, because of the low atmospheric evaporative demand caused by the low temperature [57,58,59]. The medium and long time-scale SPEI of April and May have considered the water supply condition in winter, so they show higher relationship with the winter wheat yield in the north and central part of the NCP. However, in the south part of the NCP, the precipitation and temperature conditions are more suitable for winter wheat growth than those at the north and central region of the NCP. The more suitable climate conditions lead to a short time-scale SPEI that can directly represent the soil water content, so in the south region of the NCP, short time-scale SPEI has high correlations with winter wheat yield. Meanwhile, the correlations between winter wheat yield and SPEI in the southern region are not significant, which indicates that the main restricted factor of winter wheat production in this region is not drought stress, as some previous studies have found [60]. By counting the number of winter wheat growing season with extreme moist degree at each station based on the SPEI, we also found that the stations where extreme moist occurred are mainly distributed in the southern part of the NCP (Figure S7). It indicates that excessive precipitation in some years may adversely affect wheat production in the south part of the NCP.

4.2. Global Warming Enhances the Role of Temperature in Driving the Response Patterns of Winter Wheat Yield to Drought Compared with Other Climatic Factors

Studies focusing on the driving factors of natural vegetation activities and crop yield responses to the different time-scales of drought have revealed that climate characteristics may be the main controller of the different responses [31,46,61]. Those studies suggested that the water balance (precipitation minus PET) and precipitation are usually the most influential of the different climatic variables. Generally, the different response patterns to the different time-scale SPEI could be explained by the different resistance to water deficiency between the different vegetation [62] and the varied vegetation strategies for coping with drought [63]. As in previous studies, the importance of the spatial differences in water balance, precipitation, and PET to the winter wheat yield responses to drought was also found in this study. However, compared with above three climatic factors, temperature plays a more import role in influencing the different spatial response patterns of winter wheat yield to drought in the NCP.

Some prior studies have also emphasized the importance of temperature in influencing crop yields. Lobell et al. (2011) pointed out that the majority climate influences on crop yields were driven by temperature trends rather than the rainfall trends in most regions of the world [64]. Schauberger B. et al. (2017) [65] research found that water stress caused by high temperature is the main driving force of the yield decline. By sensitivity analysis, Leng G. et al. (2019) [18] also revealed that temperature plays an important role in determining the impacts of drought under global warming. A series of studies in the NCP have found that the temperature of the winter wheat growth season has risen obviously, while precipitation has not changed significantly [66,67]. The length of the winter wheat growth period is susceptible to temperature [68]. The reproductive growth duration of winter wheat has extended because of the shift in the flowering date caused by significant warming trends [67,69]. Thus, the increasing temperature has increased the probability of winter wheat suffering from drought during the critical growth stage in the NCP. On the other hand, atmospheric water demand increases with temperature as an immediate effect [65]. The above studies may be used to explain why temperature has become increasingly important in affecting the response of winter wheat yield to drought. Although a large number of studies on how temperature affects crop production and food security have been carried out and have reached different conclusions [65,70], how temperature rise affects crop yield responses to drought requires further research and analysis against the backdrop of global warming.

4.3. The Contributions and Limitations of Our Study

Effective drought monitoring and management is becoming increasingly essential in the context of climate change. Selecting the appropriate time scale for a drought indicator (SPEI, etc.) is essential for a reasonable assessment of the influence of drought on crop yield. Our results contribute to our understanding on the response patterns of winter wheat yield to drought in the NCP. Such understanding can help us to choose a suitable time scale SPEI to evaluate the drought influence on winter wheat yield. In addition, our findings emphasize the importance of temperature in driving the response patterns of winter wheat yield to drought, this could provide references for choosing a reasonable sowing time and suitable wheat varieties.

It is important to note there are several limitations in our study. Firstly, though SPEI has been widely used in exploring the drought impacts on crop production in the NCP according to previous studies [16,17]. However, there are still limitations for the SPEI to monitor the drought condition in the irrigated area. Some drought indices which consider the irrigation influences, have been proposed [69]. The further study should collect more irrigation data and use these indices to evaluate the drought response characteristics. Secondly, the EPIC crop model was used in our study. However, there are only 16 agrometeorological stations with enough data to verify the crop model, for other stations with incomplete data, we use the crop model parameters of the site closest to it, which may reduce the simulation accuracy of winter wheat yield.

5. Conclusions

In this research, we investigated the responses of winter wheat yield to different time-scale droughts and then explored the climatic factors which may determine the different response patterns. Our results suggested that (i) the responses of winter wheat yield to different time-scale droughts have obvious spatial differences from the north part to the south part in the NCP. In the north part of the NCP, the long time-scale (9–12 months) droughts in the key growth periods (April and May) usually have the greatest impact on the winter wheat yield. In the central part of the NCP, the medium time-scale (6–9 months) droughts are more likely to affect wheat yield. However, winter wheat planted in the south part of the NCP were more sensitive to the short time-scale (1–3 months) droughts. (ii) The different patterns of winter wheat yield responses to different time-scale droughts are mainly controlled by the climate conditions (including mean temperature, precipitation, and water balance) in winter in the NCP. Global warming enhances the role of temperature in driving the response patterns of winter wheat yield to drought. Compared with the water balance, the temperature plays a more important role in driving the response pattern characteristics. (iii) The water availability and PET also affect the responses of winter wheat yield to drought. Winter wheat planted in the humid environments are easily influenced by shorter time-scale drought, while winter wheat grown under dry conditions are more sensitive to longer time-scale drought. In the context of global warming, our study can provide a reference on how to reduce drought influence on winter wheat yield and the results are also effective at sustaining long-term winter wheat productivity in the NCP.