1 Introduction

The global mean surface temperature has increased by 0.85 °C from 1880 to 2012 (IPCC 2013). Under the background of global warming, the occurrence of extreme events has increased (Chen et al. 2017; Guo et al. 2016; Peña-Gallardo et al. 2018). As one of the most damaging and widespread extreme events, drought negatively affects water resources, ecosystems, agricultural production, and sustainable socioeconomic development (Deng and Chen 2016; Fu et al. 2019; Wang et al. 2019). Drought is a complicated phenomenon influenced by the integrated effects of multiple factors (Guo et al. 2018).

The droughts have raised enormous concern regarding the occurrence, magnitude, and impacts of drought (Zhang et al. 2017). Numerous specialized drought indices have been proposed and applied for drought monitoring and assessment, e.g., the Palmer drought severity index (PDSI) (Palmer 1965), the standard precipitation index (SPI) (McKee et al. 1993), and the standardized precipitation evapotranspiration index (SPEI) (Vicente-Serrano et al. 2010a). Considering the necessity of assessing drought at multiple timescales, the SPI was developed for drought monitoring and analysis (Vu et al. 2015). Nevertheless, the calculation of SPI is based only on precipitation data and does not consider atmospheric evaporative demand (Zhu et al. 2015). SPEI combines the sensitivity of the PDSI to changes in evaporative demand with the multitemporal nature of the SPI (Vicente-Serrano et al. 2018). Recently, the SPEI has been widely used to study the variability and impacts of drought under warming conditions in many regions of the world (Ayantobo et al. 2017; Deo and Sahin 2015; Manzano et al. 2019). SPEI is an effective tool for monitoring systems that provide important information to improve disaster management (Li et al. 2019; Zhang et al. 2019b).

Drought is influenced by multiple factors, such as potential evapotranspiration (PET), precipitation (P), temperature, and total water storage (Ding et al. 2011). PET and P are key hydroclimatic variables that can directly affect floods, droughts, and water resources (Zhang et al. 2019b). The spatiotemporal variations in PET and P are essential to changes in a climate system (Yang et al. 2019; Yuan et al. 2019). The SPEI is based on PET and P, detecting drought conditions (Beguería et al. 2014; Vicente-Serrano et al. 2010a). Vicente-Serrano et al. (2010a) showed that the SPEI was more sensitive to P than to PET globally. The SPEI relies on two assumptions: the variability of PET and that of P (Vicente-Serrano et al. 2010b). At present, an increasing number of studies are using the SPEI to evaluate drought severity at different timescales (Gouveia et al. 2016; Liu et al. 2017). For example, Yao et al. (2018) applied 3-month, 6-month, and 12-month timescales of SPEI to describe meteorological, agricultural, and hydrological droughts in Xinjiang, China. Liu et al. (2017) studied the response of vegetation to meteorological drought at different timescales. Thus, to better investigate the correlation of SPEI with PET and P, it is meaningful to conduct a comprehensive analysis at multiple timescales.

The Huang-Huai-Hai Plain is one of the major grain production regions in China (Li et al. 2017) and is very prone to drought. Wang et al. (2015) found that the annual drought severity and duration both presented decreasing trends on the Huang-Huai-Hai Plain. Li et al. (2017) pointed out that the plain had experienced reduced droughts of shorter duration and of weaker severity and intensity. However, drought is expected to increase in frequency, duration, severity, and intensity from 2010–2099 under the future representative concentration pathway 8.5 (high emission) scenario. Dai et al. (2020) also suggested that most irrigation districts would experience extended drought durations over the Huang-Huai-Hai Plain under the RCP 8.5 scenario. Therefore, understanding drought characteristics and the sensitivity of drought to climate change is essential for reducing agricultural vulnerability in this region (Mei et al. 2013; Yang et al. 2015).

The primary objective of this study is to explore the spatiotemporal variations of droughts based on the SPEI from 1961–2015. The correlations of SPEI to PET and P were also analyzed at different timescales. A good understanding of the behavior of drought on the plain will be achieved by this study, and useful information for environmental protection and socioeconomic development will be provided.

2 Materials and methods

2.1 Study area

The Huang-Huai-Hai Plain, with an area of 3 × 105 km2, is the second-largest plain in China. It is located in the eastern part of China, ranging from 31° 36′ N to 40° 29′ N and 112° 13′ E to 120° 53′ E (Fig. 1) (Xu et al. 2019). The plain covers many highly populated areas in five provinces (Hebei, Shandong, Henan, Anhui, and Jiangsu) and two administrative cities (Beijing and Tianjin) (Wu et al. 2019). It is mainly formed by the sedimentation and river source effects of the Yellow River, Huaihe River, Haihe River, and Luanhe River (Liu et al. 2018). The downstream region of the Yellow River extends across the central plain and divides it into two parts: the Haihe Plain in the north and the Huanghuai Plain in the south (Hu et al. 2010). The area is located in a warm temperate zone with a strong impact from the East Asian Monsoon (Xiao et al. 2018). The annual mean precipitation is approximately 500–900 mm. Due to the continental monsoon climate, precipitation mainly occurs in summer, with less precipitation in spring and winter. The annual mean temperature on the plain ranges between 8 and 15 °C (Chen et al. 2019b). Additionally, two of the major provinces, Henan and Shandong, have been facing a dramatic decreasing trend in total water resources starting in the twenty-first century (Wang et al. 2019; Zhou et al. 2020). The amount of total water resources in Hebei Province has changed little, but the approximately 1.8 × 1010 m3 of reserve water is still far less than the average on the plain (Su et al. 2020; Yang et al. 2016). This indicated that Hebei Province has frequently been subjected to droughts (Shiau et al. 2007). The plain has a flat terrain with loam and sandy soil types, as the alluvial plain has mainly developed through the intermittent flooding of the Yellow River (Ye et al. 2012). It is the main production area for agricultural crops in China, which makes the plain an ideal test location for monitoring droughts and their ecological and economic impacts (Xiao et al. 2014).

Fig. 1
figure 1

DEM and meteorological stations on the Huang-Huai-Hai Plain

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2.2 Data

The SPEI used in this study was derived from SPEIbase v2.5 (http://spei.csic.es/database.html). SPEIbase v2.5 is based on CRU TS 3.24.01 input data from the Climatic Research Unit (CRU) of the University of East Anglia (http://badc.nerc.ac.uk/browse/badc/cru/data/cru_ts_3.24.01). This dataset has the timescales between 1 and 12 months with a spatial resolution of 0.5° × 0.5°, and its temporal coverage is between January 1901 and December 2015. The calculation of the PET in SPEIbase v2.5 is based on the FAO-56 Penman-Monteith method. P data were obtained from the CRU TS3.24.01 dataset. Um et al. (2020) showed that PET was predominant in drought phenomena in various geographic regions based on data from CRU and the National Centers for Environmental Prediction (NCEP). The results obtained from the two datasets appear to be slightly different. Van der Schrier et al. (2013) calculated the self-calibrating PDSI for the period 1901–2009 based on the CRU TS 3.10.01 datasets and found a trend toward drying conditions in some parts of the world during 1950–1985.

We used observed data to verify the reliability of SPEIbase v2.5 data in terms of spatiotemporal performances of SPEI in the plain. The SPEI was calculated based on the monthly precipitation and temperature from 43 meteorological stations during 1961–2015. The monthly precipitation and temperature were obtained from the China Meteorological Data Service Center (http://data.cma.cn).

2.3 Methods

2.3.1 Mann–Kendall nonparametric test

The Mann–Kendall (M–K) test is based on the correlation between the relative ranking of values in a time series and their chronological order (Kendall 1975; Mann 1945). The M–K test is widely used to detect trends in hydrometeorological time series, such as trends in P, PET, temperature, and drought index (Ye et al. 2019; Zhao et al. 2019). The M–K statistic S is used to estimate the significance as follows (Dietz 1981; Hirsch et al. 1982; Lettenmaier 1988):

$$ S=\sum \limits_{i=1}^{n-1}\sum \limits_{j=i+1}^n\operatorname{sgn}\kern0.4em \left({x}_j-\operatorname{}{x}_i\right) $$
(1)
$$ \operatorname{sgn}\kern0.4em \left(\theta \right)=\left\{\begin{array}{c}1\\ {}0\\ {}-1\end{array}\right.{\displaystyle \begin{array}{c}\left(\theta >0\right)\\ {}\left(\theta =0\right)\\ {}\left(\theta <0\right)\end{array}} $$
(2)

where q is the number of tied groups and tp is the size of the pth item in the m group. S is expected to have an N (0, var(S)) distribution (Jung et al. 2011).

The Mann–Kendall test statistic ZMK is estimated as follows:

$$ {Z}_{MK}=\left\{\begin{array}{c}\frac{s-1}{\sqrt{\operatorname{var}(S)}},S>0\\ {}0,S=0\\ {}\frac{s+1}{\sqrt{\operatorname{var}(S)}},S<0\end{array}\operatorname{}\right) $$
(4)

where ZMK is a standard normal variable. An above zero (below zero) value of ZMK illustrates that the data show a positive (negative) trend over time. The null hypothesis H0, that ZMK is not statistically significant or shows no significant trend, accepted if − Z1−α/2 ≤ Zc ≤ Z1−α/2, where ± Z1−α/2 are the standard normal deviates and α is the significance level for the test (Jung et al. 2011; Zhao et al. 2019).

2.3.2 Pearson’s correlation analysis

To evaluate the correlation of climate factors to variations in SPEI, the spatial correlations between the SPEI and the driving factors of drought were examined by calculating Pearson’s correlation coefficient for all grid cells (Xu et al. 2006).

3 Results

3.1 Comparison between SPEIbase v2.5 and the observed SPEI

The Pearson correlation coefficient (R), mean absolute error (MAE), and normalized root mean squared error (NRMSE) were used to quantitatively compare the performance of the SPEIbase v2.5 and observed SPEI at different timescales (Fig. 2). R was used to evaluate the degree of correlation between the SPEIbase v2.5 and the observed SPEI. The MAE reflects the average error between the SPEI product and the observed SPEI. NRMSE refers to the normalized root mean square deviation or error. When the value is close to zero, it represents less errors. When the NRMSE was higher than 0.3, the product estimates were considered unreliable. The results showed that the four groups of data presented significant linear correlations (Fig. 2), with correlation coefficients of 0.89, 0.88, 0.88, and 0.87, respectively. SPEI-01 had the highest correlation coefficient (0.89), compared with those of the other three timescales (Fig. 2a). In addition, SPEI-01 had the lowest NRMSE (0.07) and the smallest MAE (0.34) among the four timescales. Compared with those of SPEI-01, SPEI-03 and SPEI-06 had higher MAE and NRMSE, and slightly lower R (0.88). SPEI-12 exhibited a higher NRMSE (0.12) and the highest MAE (0.39), indicating that gridded SPEI-01 performed better than SPEI-12 (Fig. 2a, d). Overall, the SPEIbase v2.5 values were significantly correlated with the observed SPEI and demonstrated good spatial performance.

Fig. 2
figure 2

Evaluation of the performance of SPEIbase v2.5 on the Huang-Huai-Hai Plain during 1961–2015. a 1-month, b 3-month, c 6-month, and d 12-month timescales. The blue and red oblique dash lines denote a 1:1 line and a least-squares regression line, respectively

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Figure 3 shows the temporal performances of SPEIbase v2.5 compared with the observed SPEI at the four timescales during 1961–2015. SPEIbase v2.5 correctly reflected the general patterns of the four timescale variations in the observed SPEI during 1961–2015. In particular, SPEI-01 and SPEI-03 from SPEIbase closely followed the fluctuations of the observed SPEI and exhibited strong temporal similarity (Fig. 3a, b). Thus, SPEIbase v2.5 can be applied to analyze spatiotemporal variations in drought intensity and the sensitivity of the SPEI to climate factors in the study area.

Fig. 3
figure 3

The temporal comparison of the monthly SPEI from SPEIbase v2.5 against the observed SPEI from 1961–2015. a 1-month, b 3-month, c 6-month, and d 12-month timescales. The red line represents SPEIbase v2.5, and the blue line represents the observed SPEI

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3.2 Temporal-spatial variations in droughts

Figure 4 shows the temporal evolution of the SPEI based on grids at different timescales from 1901 to 2015 (i.e., SPEI-01, SPEI-03, SPEI-06, and SPEI-12). The fluctuations in SPEI-01 were frequent, without considering the influence of relatively longer preceding precipitation, and were susceptible to rapid climatic variations (Fig. 4a). The amplitudes of the SPEI-03, SPEI-06, and SPEI-12 fluctuations in the time series were smaller than those of the SPEI-01 fluctuations in the time series (Fig. 4b, c, d). As the timescale increased, the amplitude and the frequency of the fluctuations decreased, indicating that the separations between dryness and wetness became clearer (Fig. 4). Changes of precipitation and temperature can make the SPEI fluctuate, which is a reasonable sign of drought conditions (Du et al. 2013; Wang et al. 2018).

Fig. 4
figure 4

Temporal variations in SPEIbase v2.5 from 1901–2015 on the Huang-Huai-Hai Plain. a 1-month, b 3-month, c 6-month, and d 12-month timescales. The blue line represents the SPEI value, and the red line represents an SPEI value of − 1.5

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According to the classification of SPEI values, an SPEI value between − 2 and − 1.5 is defined as severe drought, and a value below − 2 is defined as extreme drought at a given station/grid. At the 1-month and 3-month timescales, numerous SPEI values were between − 2 and − 1.5. Among them, the SPEI values reached their lowest values in 2001 (SPEI-01) and 1917 (SPEI-03), at − 1.76 and − 1.92, respectively (Fig. 4a, b). At the 6-month timescale, the lowest value was − 2.27 in 1916, representing extreme drought conditions (Fig. 4c). Severe drought also occurred in 1919 at the 12-month timescale, reaching − 1.96 (Fig. 4d). These results clearly indicate severe drought conditions occurred around the 1920s according to 3-, 6-, and 12-month SPEI.

Figure 5 shows the spatial pattern of the SPEI at various timescales from 1901 to 2015, displaying distinct distribution characteristics from north to south. As the timescale increased, the value of SPEI decreased from 0.006–0.014 (SPEI-01) to − 0.004–0.007 (SPEI-12) (Fig. 5a, d). The SPEI values were low in the middle and southern part of the plain at each timescale. In contrast, high SPEI values were located in the north (Fig. 5a–d).

Fig. 5
figure 5

The spatial pattern of SPEIbase v2.5 from 1901–2015 on the Huang-Huai-Hai Plain. a 1-month, b 3-month, c 6-month, and d 12-month timescales

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The Mann–Kendall method and Sen’s slope were applied to detect trend variations in each grid from 1901 to 2015 on the plain (Fig. 6). The spatial variations of SPEI-01, SPEI-03, SPEI-06, and SPEI-12 showed local drying trends (16.6%, 0.4%, 1.4%, and 13.4% of the plain, respectively) and wetting trends (83.4%, 99.6%, 98.6%, and 86.6% of the plain, respectively) during 1901–2015. The spatial pattern of SPEI-01 was relatively complex. A drying trend was obvious in the western region (Fig. 6a). Specifically, the southern part of this region presented a significant wetting trend with relatively large slope values at the SPEI-03 and SPEI-06 timescales (Fig. 6b, c). The slope values of the 12-month SPEI obviously decreased in the northern part of the plain but the slope values in the southern region increased (Fig. 6d). It can be concluded that more than 70% of the total grids experienced wetting trends at each timescale (Fig. 6). The plain with significant wetting trends mainly located in the south, accounting for approximately 9.7% of the total grids for SPEI-01, 23% for SPEI-03, 17% for SPEI-06, and 8.8% for SPEI-12. Twelve-month SPEI characteristics indicated that drying trends existed in the northern parts of the plain. Overall, drought was being alleviated due to the significant wetting trends in most regions. Similar results were found by Wang et al. (2015), who pointed out that the wetting trends may have been caused by increased precipitation under global warming. In addition, the alleviation of drought may be attributed to an increase in aerosols, which decrease solar radiation and reduce PET (Gao et al. 2006).

Fig. 6
figure 6

The spatial pattern of Sen’s slope of the SPEIbase v2.5 from 1901–2015 on the Huang-Huai-Hai Plain. The red dot represents that the trend is significant at the 0.05 significance level. a 1-month, b 3-month, c 6-month, and d 12-month timescales

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3.3 Influence of PET and P on SPEI

We conducted the sensitivity of the SPEI to PET and P to quantitatively explain the mechanisms of droughts. The sensitivity of the SPEI to PET was assessed as the negative correlation between the SPEI-01, SPEI-03, SPEI-06, and SPEI-12 with the cumulative 1-month PET, 3-month PET, 6-month PET, and 12-month PET, respectively (Fig. 7). At the 1-, 3-, and 6-month timescales, the SPEI had a low correlation coefficient with PET. At the 12-month timescale, the most significant correlation coefficient was − 0.57 at given grids of the eastern plain. All the grids exceeded the 0.05 significance level at the 12-month timescale. The correlation coefficient between SPEI-12 and 12-month PET was the highest, which was determined by the algorithm used to estimate the duration factors for the calculation of the SPEI (Zhang et al. 2019a). Thus, the SPEI was influenced by PET, especially at the 12-month timescale.

Fig. 7
figure 7

Pearson’s correlation coefficient between SPEI and PET at different timescales at the grid cell level on the Huang-Huai-Hai Plain during 1901–2015. a 1-month, b 3-month, c 6-month, and d 12-month timescales (all grids are at the 0.05 significance level at the 12-month timescale)

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Pearson correlation analysis was also conducted between SPEI and P in this study (Fig. 8). At the 1-month timescale, the SPEI and P showed a higher correlation in the southern parts of the plain than in the north, with a correlation coefficient of 0.68. The P in the northern parts of the plain had little impact on SPEI, and the correlation coefficient was 0.35 (Fig. 8a). At the 3-month timescale, the correlation coefficient between the SPEI and P was higher in the south (0.59) than in the north (0.30) (Fig. 8b). In terms of the 6-month timescale, the correlation coefficient increased from the north (0.36) to south (0.68) (Fig. 8c). In addition, the highest correlation coefficient of approximately 0.99 expanded to cover almost all regions of the study area at the 12-month timescale (Fig. 8d). As the timescale changed from 1 to 12 months, the correlation coefficient between SPEI and P increased. And the correlation coefficients of 1-, 3-, and 6-month timescales presented similar spatial distribution characteristics, with higher correlation coefficients in the south and lower in the north.

Fig. 8
figure 8

Pearson’s correlation coefficient between SPEI and P at different timescales at the grid cell level on the Huang-Huai-Hai Plain during 1901–2015. a 1-month, b 3-month, c 6-month, and d 12-month timescales (all grids are significant at the 0.05 significance level at the 1-, 3-, 6-, and 12-month timescales)

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4 Discussion

The SPEI is based on the monthly differences between P and PET, which represents a simple climatic water balance condition (Vicente-Serrano et al. 2010a). The mean Pearson’s correlation coefficients between SPEI and PET (or SPEI and P) were compared at different timescales (Fig. 9). Higher correlations were found between the SPEI and P than between the SPEI and PET at the same timescale. The correlation coefficient between SPEI and PET (and P) on the 12-month timescale was the highest, which indicated that the SPEI was susceptible to PET and P on long timescale. Zhang et al. (2019a) confirmed that the SPEI algorithm can incorporate both PET and P data for an unspecified period but corresponded best to the most recent 9–12 months. Previous conditions were incorporated because the long-term drought was cumulative, so the correlations between SPEI and PET and P at a particular time were dependent on the current and cumulative conditions from previous months (Zhang et al. 2019a). Thus, the SPEI was highly correlated with PET and P at the lengthier timescale.

Fig. 9
figure 9

Mean Pearson’s correlation coefficients between SPEI and P (and PET) at different timescales (1, 3, 6, and 12 months) on the Huang-Huai-Hai Plain

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Figure 10 shows that the spatial characteristics of the SPEI values were related to PET and P at the 12-month timescale. The areas with higher SPEI values were located in the southern parts of the plain (Fig. 10a). Higher P and lower PET values were also observed in the southern parts of the plain (Fig. 10b, c). In certain areas of the southern plain, both the SPEI and P showed significant increasing trends (Fig. 10 d and f). The SPEI, PET, and P all showed upward trends in the southwestern regions (Fig. 10 d, e, and f). The upward trend in the SPEI represented a wetting trend. The conditions still tended to represent wetting even with an upward trend in PET. The increasing amount of P might be the cause of the small correlation between SPEI and PET. Yao et al. (2018) confirmed that P was the main factor causing droughts. At the 12-month timescale, the value of SPEI in most areas of the plain might be explained by the diverse hydroclimatic conditions and by the combined effects of PET and P (Vicente-Serrano et al. 2015).

Fig. 10
figure 10

Mean values of a SPEI, b PET, c P, and variation trends in d SPEI, e PET, and f P at the 12-month timescale determined by the Mann–Kendall trend test at the grid cell level on the plain during 1901–2015. The symbol represents an upwards trend with p ≤ 0.05

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The SPEI was more sensitive to P than to PET on the Huang-Huai-Hai Plain; this was likely because the SPEI included the sensitivity of the changes in the precipitation in its calculation and was influenced by the standardization of anomalies in the soil water budget (Ling et al. 2019). The SPEI may be more sensitive to PET than to P in other areas (Vicente-Serrano et al. 2010a; Zhang et al. 2019b). The correlation of SPEI with either PET or P was not high in certain regions with particular topography, such as areas susceptible to the high altitude, and other variables should also be taken into account (Paulo et al. 2012).

The SPEI can be used to identify drought conditions and to capture the responses of climate variables to drought (Vicente-Serrano et al. 2018). Therefore, multiple climate variables (e.g., runoff, temperature, and soil moisture) may play important roles in explaining drought conditions and may have effects on the SPEI (Zhang et al. 2017). There is widespread recognition that global warming increased hydrologic climatic extremes (Chen et al. 2019a; Li et al. 2020). A significant positive correlation was observed between runoff and SPEI (Yao et al. 2018). Minimal runoff, high temperature, and a lack of precipitation led to reductions in soil moisture (Ling et al. 2020; Zhang et al. 2020), which was more likely to induce drought (Guo et al. 2013). SPEI showed the highest correlation with soil moisture among the different drought indices, e.g., SPI, SPEI, and PDSI (Vicente-Serrano et al. 2012). As the plain was an agricultural region characterized by frequent droughts, both sufficient surface water and groundwater played active roles to ensure food supply (Tang et al. 2018; Wang et al. 2015). The SPEI had a good correlation with surface water and groundwater (Vicente-Serrano et al. 2012). Notably, other factors should also be considered among the environmental factors related to the SPEI. We mainly focused on the sensitivity of the SPEI to PET and P in this study. A comprehensive consideration of the climate factors associated with the SPEI will improve our understanding of droughts (Marvel et al. 2019). We only used the CRU data in this present study. Various data such as Climate Forecast System Reanalysis (CFSR), Climatologies at High Resolution for the Earth’s Land Surface Areas (CHELSA), and European Environment Agency (ERA5) climate reanalysis data produced by ECMWF should also be considered in future studies to compensate for the errors and uncertainties introduced by using only the CRU data.

5 Conclusions

The spatiotemporal characteristics of drought and the sensitivity of SPEI to the related climate factors were investigated based on SPEIbase v2.5 on the Huang-Huai-Hai Plain of China from 1901 to 2015. The SPEI showed high values in the northern parts of the study area, and a significant wetting trend was observed in the southern regions. The changes in P were the dominant driving factors for the SPEI at different timescales. In addition, the correlation coefficients between the SPEI and PET and P were the highest at 12 months on the Huang-Huai-Hai Plain. Overall, the use of the SPEI is beneficial for the assessment and quantification of droughts on the Huang-Huai-Hai Plain in China. The present study provides evidence that improves our understanding of the climate variation related to drought.