Spatial-temporal characteristics of meteorological drought and its relationship with circulation indices over Songhua River Basin, China

Droughts are natural disasters caused by uneven spatial and temporal distribution of precipitation, increased evapotranspiration, and inadequate water supply (Augustine & Lin 2023) and characterised by long duration, high occurrence frequency, and wide impact range (Rahman & Lateh 2016; Tong et al. 2017). Droughts can be categorised as meteorological, hydrological, agricultural, and socio-economic, with meteorological droughts representing one of the drivers of other forms of drought (Gumus et al. 2023). The study points out that the frequency and intensity of meteorological drought events caused by global warming will continue to increase in the future (Fung et al. 2020). Therefore, in the context of global climate change, it is of great significance to investigate the evolution of meteorological droughts at the regional scale to achieve sustainable development.

Given the difficulty of quantifying the intensity and frequency of droughts and accurately monitoring changes in these factors, scholars worldwide have developed a variety of drought indicators to meet the needs of research and applications in different fields (Wondimu et al. 2023; Yang et al. 2023). Among them, the Palmer drought severity index (PDSI; Palmer 1965) is based on the principle of water balance and considers the effects of factors such as the supply and demand of actual moisture on meteorological drought; however, it is not spatially comparable. The standardised precipitation index (SPI; McKee et al. 1993) only considers changes in precipitation and ignores changes in evapotranspiration caused by temperature rise in the meteorological drought, which represents a limitation for studies on drought in the context of climate warming. In addition, the standardised precipitation evapotranspiration index (SPEI; Vicente-Serrano et al. 2009) combines the advantages of the PDSI and SPI indices and considers the effects of temperature changes and water balance on drought while calculating the multi-scale characteristics of drought. The SPEI has been widely applied in the study of meteorological drought. Studies in Bangladesh (Mohammad et al. 2022) and Sichuan Province, China (Liu et al. 2021) showed that the SPEI has better applicability than the SPI, and research in the Java Island region (Suroso et al. 2021) and northeastern China (Shen et al. 2017) revealed that the SPEI can accurately characterise drought events.

In recent years, most studies on meteorological drought have used methods such as linear fitting or wavelet transform to analyse the associated change trends, and these methods assume the linearity and stationarity of the time series (Tong et al. 2017; Ye et al. 2019). However, the inherent non-linear characteristics of meteorological factors will cause deficiencies in the linear fitting of climate element time series trends, and studies have shown that changes in meteorological drought are affected by the non-linear characteristics of climate factors (Song et al. 2020; Wu et al. 2023). As one of the most recent methods developed to analyse the trends and cycles of time series, the Ensemble Empirical Mode Decomposition (EEMD; Huang & Wu 2008) method can determine the inherent trends of non-linear and non-stationary time series and determine the inherent trend of non-linear and non-stationary time series during meteorological drought (Li et al. 2015; Liu et al. 2020) and precipitation changes (Guo et al. 2016). Thus, it has been widely used in trend and cycle studies.

In addition to being affected by regional environmental factors, drought events are also impacted by large-scale atmospheric and ocean circulation parameters (Li et al. 2015; Manzano et al. 2019). Atmospheric circulation factors can affect the mass, heat, and momentum in the atmosphere, thereby causing climate anomalies (Wang et al. 2020). Previous research has shown that the Pacific Decadal Oscillation (PDO), North Atlantic Oscillation (NAO), Arctic Oscillation (AO), and Southern Oscillation Index (SOI) are strongly correlated with meteorological drought in the Liaohe River Basin in China (Chen et al. 2023a); precipitation in northeastern India is closely related to the Atlantic Multidecadal Oscillation (AMO), El Niño Southern Oscillation (ENSO), and PDO (Singh et al. 2020); and precipitation in Northeastern China is affected by the NAO and PDO, and NAO and PDO in turn affect drought (Zeng et al. 2019). Therefore, the atmospheric circulation index may have a direct or indirect impact on drought, and it is important to analyse its intrinsic relationship with drought events.

The Songhua River Basin (SRB) is located in northeastern China in a temperate continental semi-humid and semi-arid monsoon climate zone, and it represents one of the seven major river basins of China, and it is an important grain-producing area and commercial grain production base in China (Yu et al. 2023). As one of the regions in China most affected by global climate change, the SRB experiences frequent droughts (Ye et al. 2019). The risk of drought in SRB will increase in the future under the continued threat of global warming (Abrar et al. 2018, 2019; Wu & Zhang 2018). Therefore, studying the evolution of meteorological drought in SRB is important for developing adaptation strategies to reduce drought losses. However, the detailed study of meteorological droughts in each subregion of the basin has not yet been carried out, and the non-linear trend and periodical characteristics of meteorological droughts as a result of climate factor fluctuations are not yet clear, and the influence of atmospheric circulation factors on meteorological droughts in the basin is still not clear.

This study focuses on SPEI time series data and uses the EEMD method and Pettit mutation to analyse the trends, periods, and mutation characteristics of the SPEI data. Moreover, the spatial distribution of droughts at different time scales is assessed based on the drought frequency and intensity, and the relationship between drought events and circulation indices is discussed. This study provides insights for performing detailed assessments of drought in the SRB and conducting effective drought monitoring.

The SRB is located between 119°52′–132°31′ E and 41°42′–51°38′ N and spans the three provinces of Inner Mongolia, Heilongjiang, and Jilin. The basin is 1,070 km wide from north to south and 920 km long from east to west and has a total watershed area of 55.68 × 10⁴ km². The basin has a substantial seasonal temperature difference, with the multi-year average temperature ranging from 3–5 °C. The spatial and temporal distribution of precipitation in the basin is relatively uneven, and the average annual precipitation is approximately 500 mm. Precipitation is mainly concentrated in June to September, accounting for approximately 60–80% of the annual precipitation. The SRB was divided into five subregions according to differences in topography and geomorphology, considering the ecological environment and socio-economic factors as shown in Supplementary Figure S1(b) (Zhang et al. 2019). The main drought trends in the basin were analysed on a subregional basis, which is important for basin zonal drought variability and multi-regional joint studies. Supplementary Figure S1(a) shows the location of the SRB and its elevation is shown in Supplementary Figure S1(c).

Meteorological data for the SRB from 1960 to 2019 were derived from the China Surface Climatological Data Daily Value Dataset (V3.0) (https://data.cma.cn/) and include the daily average air temperature, maximum air temperature, minimum air temperature, daily rainfall, latitude, and longitude. The data were processed as follows. Station data included in the study were no less than 60 years old, and stations with more than 5% missing data or more than 30 consecutive days without data collection were excluded. Data interpolation was conducted to supplement the data when part of the data was missing. Data from 35 meteorological stations in the SRB were obtained and used for calculations and analyses. The atmospheric circulation data from 1960 to 2019 used in this paper have a temporal resolution of monthly scale, and the corresponding seasonal and annual scale data were calculated by averaging the monthly scale data and analysed for correlation with the SPEI of the same period, including the AO, Indian Ocean Dipole (IOD), SOI, and Western Pacific Remote Correlation (WP) (http://www.noaa.gov/). The underlying spatial data were derived from the Geospatial Data Cloud 30 × 30 m resolution digital elevation model (https://www.gscloud.cn/) and National Zone Boundary Vector Data (https://www.craes.cn/).

The SPEI is an indicator used to assess the probability of the difference between precipitation and evapotranspiration in a given period (Vicente-Serrano et al. 2009). It considers the response of precipitation and evapotranspiration to drought and is suitable for monitoring and assessing droughts at different time scales in semi-arid and semi-humid regions. The specific calculation procedure is described in Liu et al. (2020). The four seasons were divided according to the meteorological seasons, meaning that March–May was spring; June–August was summer; September–November was autumn; and December–February was winter. Drought categories were classified based on relevant studies as shown in Supplementary Table S1 (Wang et al. 2018).

The EEMD is a signal processing and data analysis method (Huang & Wu 2008) developed based on empirical mode decomposition (EMD) (Huang et al. 1998; Wu & Huang 2004). It addresses the problems of modal aliasing and instability in the application of the EMD method and is suitable for analysis of non-smooth and non-linear time series as an adaptive non-linear signal decomposition method. This method mainly expresses the temporal distribution of the data by extracting the intrinsically correlated energy of the time scale and generating a set of intrinsic mode functions (IMFs) and residual (R) (Wu & Huang 2011). Also, all conclusions of this study are based on this non-linear trend of the meteorological drought after EEMD decomposition.

The specific procedures of EEMD can be summarised as follows:

• Step 1: Input the target data as the original signal ⁠.

• Step 2: Set the EEMD parameters, including the noise standard deviation ⁠, number of realizations ⁠, and maximum number of sifting iterations allowed ⁠.

• Step 3: Conduct the decomposition. Add a normally distributed white noise series with finite amplitude to the given signal ⁠, and reconstruct a new set of series using Equation (1):

  

  (1)
• Step 4: Decompose into n levels of IMFs and a trend term for the decomposition by EMD using Equation (2):

  

  (2)

  where is the IMF after the decomposition.

• Step 5: Repeat steps 2 and 3 with different white noise series until the maximum number of realizations is achieved for i.

• Step 6: Obtain IMFs by calculating the ensemble means of the corresponding IMFs to eliminate mode mixing. The final results are given by Equations (3) and (4):

  

  (3)

  

  (4)

where is the IMF, and is the trend term.

Pettitt's mutation test is a non-parametric statistical test commonly used to analyse the mutation points in a time series. It does not require sample hypothesis testing, it is suitable for a variety of time series types, and it is widely used in meteorology, environment, and finance applications, among others. The calculation process is described in Pettitt (1981). Owing to the uncertainty of meteorological changes and human activities, there may be more than one mutation point in the sequence that needs to be tested several times (Li et al. 2014a). The specific steps are as follows. The first level mutation point in the sequence should be detected using the Pettitt's method. According to the first level mutation point found, the original sequence should then be split into two, before and after the mutation of the two segments of the sequence before being tested again. If there is no new mutation point, this means that all potential mutation points have been identified. This is then used to determine the sequence segments. If a mutation point remains, these steps are repeated.

To further resolve the oscillations of different feature scales present in the original data, the variance contribution ratio and the correlation coefficient of each IMF component was calculated using the Fast Fourier Transform method. The variance contribution ratio is the extent to which each intrinsic modal function (IMF) of the original SPEI series contributes to the total variance of the original series during the EEMD. It is calculated by comparing the ratio of the variance of each IMF to the variance of the original series, the variance contribution ratio can be used to measure the importance of each IMF in explaining the variability of the original series. The correlation coefficient is a statistical measure of the strength of correlation between each IMF of the original SPEI sequence and the original sequence during the EEMD process, and by analysing the correlation between the IMF components and the original sequence, it is possible to identify those components that contain key information about the original sequence as shown in Table 1. The main periods of IMF1, IMF2, IMF3, and IMF4 were 3, 6.7, 15, and 30 years, respectively. The 3-year period of the IMF1 component had the largest variance contribution of 45.92%, with a correlation coefficient of 0.696. The IMF2, IMF3, and IMF4 components had variance contributions of 13.8, 10.5, and 23.89%, respectively, with correlation coefficients of 0.391, 0.229, and 0.501, which were significant. As shown by the variance contributions of the individual components, annual oscillations dominated the annual-scale SPEI variations, which were mainly determined by IMF1, with a main period of 3 years.

The period, variance contribution, and correlation coefficients of the components derived from the seasonal decomposition of the SPEI values are listed in Table 2. The spring SPEI values had 2.9- and 6-year periods in annual variability, with a higher percentage of variance contribution (54.77 and 36.71%, respectively). The decadal variability had 12- and 20-year periods. The main periods of the components of the summer SPEI values were 2.5 (71.96%), 5 (11.92%), 12, and 30 years, respectively. Autumn SPEI values had periods of 2.7 (71.19%) and 5.5 (14.07%) years in annual variability and 15 and 20 years in decadal variability. The main periods of the components of the winter SPEI values were 3 (54.14%), 6, 12, and 30 years (13.44%), respectively. The seasonal SPEI variations were determined by annual oscillations, and the main periods were dominated by the IMF1 component.

The year of mutation of the annual SPEI sequence in the SRB was detected using the Pettitt mutation detection method. The study period was divided according to the year of mutation, and the results of the division are shown in Supplementary Figure S2. The years of mutation in the annual SPEI sequence were 1968, 1980, 1997, and 2012. Therefore, the study period was divided into five phases: 1960–1967, 1968–1979, 1980–1996, 1997–2011, and 2012–2019. The average SPEI values at each stage were 0.204, −0.607, 0.739, −0.490, and 0.782, respectively.

In terms of temporal changes in drought, there was a mitigating trend in the annual drought in the SRB from 1960 to 2019 (Ren & Dong 2022). This was consistent with the findings of this study. Ye et al. (2019) found that droughts in the SRB are affected by the combined effects of temperature and precipitation. A sudden change in temperature in the SRB occurred around 1990, while there were 7-, 14-, and 28-year periods of temperature change that coincided with the drought period in the basin (Li et al. 2014b). The entire basin has been continuously warming and becoming wetter, which may have contributed to this result (Yu et al. 2023). However, Li et al. (2020) concluded that there was a trend of enhanced autumn drought in the SRB, which is in contrast with the results of this study. This may be related to the study being conducted in different years and the drought indices selected.

In terms of the spatial distribution of drought, the drought-high-frequency region and the drought-intensity high-value region of the SRB from 1960 to 2019 were mainly distributed in Regions I and IV. This is similar to the results of Feng et al. (2016), who found that the drought area of the SRB was mainly distributed in the northeastern and southwestern regions. Song et al. (2015) found that precipitation indices, such as intense precipitation and annual precipitation indices in the SRB, showed an upward trend over time. However, the magnitude was relatively small, with a spatial trend of gradual decrease from the southeast to the northwest. Meanwhile, the sustained dry and wet period indices such as sustained dry days were mainly distributed in the western part of the SRB side by side, reflecting the reason for the more severe drought in Region I (Yu et al. 2023).

To further resolve the relationship between drought and circulation indices, four atmospheric circulation indices (AO, IOD, SOI, and WP) were selected for correlation analysis with annual SPEI values in the SRB. Table 3 presents the period of each component after the decomposition of each circulation index. The period of each circulation index for different components is the same as the period of the corresponding components of the annual SPEI. Therefore, the Pearson correlation analysis method could be used to analyse the correlation between the SPEI and circulation indices.

This multi-temporal study of spatiotemporal variations in drought in the SRB presented certain limitations. The selection of different indicators that represent meteorological droughts is likely to affect drought events in different ways. Ren & Dong (2022) selected the SPEI as a drought indicator to study the trend of meteorological drought in the SRB and concluded that there was a weakening drought trend. This contradicts the conclusion obtained by Wu & Zhang (2018), who selected the SPI as a drought indicator, thus highlighting the differences in the method of assessing trends and variations between the SPEI and SPI (Song et al. 2020). In addition to circulation indices, the impacts of various human activities on climate change have increased in recent years, and their impacts on drought events should be further explored (Zhao et al. 2023). Data over a longer time span are required to allow for a more accurate trend analysis of drought changes in the watershed and to test the veracity of the drought trend changes obtained in this study (El Kenawy et al. 2020). In addition, with global climate change, the prediction of future meteorological droughts is a research direction that cannot be ignored. Resolving these uncertainties may provide new insights for future research on the causes of drought events.

Moreover, the EEMD method used in this study describes fluctuations in the time series and accurately identifies features such as non-linear trends and periodic oscillations in the temporal variation of drought. This represents a considerable advantage in studies on the complex changes in drought (Feng & Su 2019). Meanwhile, by using factors such as the topography of the study area to divide the study area and mutation conditions to divide the drought time period to conduct a detailed multi-temporal study of drought events in the basin, we can more accurately identify the differentiation of drought changes in different regions at different times and deepen our understanding of spatial and temporal changes in drought in the basin (Luo et al. 2023). The results of the study have enriched the research results on meteorological drought in the SRB, and provide a basis for quantitative analysis of the spatial and temporal characteristics of meteorological drought in the basin. The results of the research can provide important references for the development of agriculture in the high-frequency and high-value drought regions of the basin, the scientific formulation of drought mitigation and planning, and the effective response to drought, which is of great significance in guaranteeing the food security of the country, and the promotion of the socio-economic-ecological system.

Based on data collected from 35 meteorological stations in the SRB from 1960 to 2019, this study used the SPEI as a drought indicator, applied the EEMD method to study the non-linear trend and cyclic changes of drought, and performed Pettitt's mutation test to analyse drought mutations that divide the study period. The temporal and spatial variations of droughts in the basin were analysed in terms of drought frequency and intensity. The correlations between the SPEI and the AO, IOD, SOI, and WP were analysed using Pearson's correlation analysis and cross-wavelet analysis, and the following conclusions were reached:

• 1) The overall meteorological drought in the SRB during 1960–2019 showed periods of 3, 6.7, 15, and 30 years. There was a clear transition from drought to wetness around 1990. The SPEI time series had four mutation points based on Pettitt's mutation tests for 1968, 1980, 1997, and 2012.

• 2) During the study period, drought in the SRB showed an increasing trend in Regions I and IV and a weakening trend in Regions II, III, and V. High-frequency and high-value drought regions were mainly distributed in the watershed in Regions I and IV. The frequency of spring droughts was higher in Regions I, II, and V. The frequency of autumn droughts was higher in Regions III and IV, and the value of drought intensity was higher in each subregion. The drought frequency and intensity in each subregion showed a trend of increasing and then decreasing.

• 3) Annual-scale drought in the basin correlated more strongly with the AO and WP in spring and summer, mainly with the AO, IOD, and SOI. Drought in autumn and winter was mainly influenced by the AO and SOI.

This study analysed spatial and temporal variations in meteorological drought in the SRB based on the SPEI and examined the relationship between meteorological drought and circulation indices. The findings have highlighted the patterns of meteorological drought in the SRB and its causes, which can provide a reference for discussing drought events in other regions. However, a number of factors, including human activity, influence the formation of droughts, and future studies should further consider these additional aspects.

J.Xu: methodology, writing – original draft, formal analysis, conceptualisation. X.L.: formal analysis. J.Xue: formal analysis. X.D.: formal analysis. W.W. and G.W.: formal analysis. Q.Z.: writing – review and editing, conceptualisation, formal analysis.

This work is funded under the auspices of the National Natural Science Foundation of China (Grant Nos. 51909104, 51909105, and 41471160).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.