Three-dimensional meteorological drought characteristics and associated risk in China

Drought as a hazardous natural disaster has been widely studied based on various drought indices. However, the characteristics of droughts have not been robustly explored considering its dual nature in space and time across China in the past few decades. Here, we characterized meteorological drought events from a three-dimensional perspective for the 1961–2018 period in the mainland of China, and attributed the variation of drought intensity to its influencing factors. We further assessed associated drought risk with socioeconomic data for the 2002–2018 period. We found that drought events with high intensity, large area, and long duration are mainly distributed in western and northern China, especially in Inner Mongolia, Xinjiang, Tibet, and Qinghai. The drought intensity and affected area anomalies present a six-phase pattern of ‘negative-positive-negative-positive-negative-positive’ during 1961–2018. The intensity of drought events showed a decreasing trend but the affected area and duration showed an increasing trend in 2009–2018. Over the decades, the centers of high drought intensity and long duration tend to move eastward and northeastward, respectively. The PET variations contributes larger than precipitation variations to drought intensity variations in the arid regions while being opposite in the humid southern regions. Drought risk assessment further indicates that high drought risk areas are concentrated in northern China, including Inner Mongolia, Xinjiang, Gansu, Sichuan, Hebei, and Heilongjiang. Increasing trends in drought risk for the 2002–2018 period are detected in Inner Mongolia, Xinjiang, Sichuan, Henan, Gansu, Hunan, Shanxi, Qinghai. Our findings provide scientific guidance for policymakers to develop adaptive disaster prevention measures.


Introduction
As one of the most prevalent and extensive natural disasters, drought is threatening almost all regions in China, with about 21.28 million ha of farmland affected by drought per year (Zhai et al 2017, Song et al 2021, Zhang et al 2022).Annual direct economic losses reach more than 32 billion Yuan in China according to 2013 price levels (Song et al 2020, Zhou et al 2021).In recent years, climate change has intensified the frequency and intensity of extreme drought (Huang et al 2022, Zhang et al 2022).Major droughts especially occurred in recent 20 years have caused massive economic losses (He et al 2011, 2013, Shao et al 2018).Hence, it is essential to investigate the spatiotemporal variation of drought characteristics in China, especially their climate driving factors and associated socioeconomic risk for managing and mitigating drought impacts.
Drought is generally divided into several types (i.e.meteorological, agricultural, hydrological droughts) and in this study we focus on the meteorological drought which is generally associated with precipitation shortage (Wang et al 2022).Recently, a number of studies have examined the spatial distribution and temporal changes of meteorological drought characteristics over China for the whole country (Yao et al 2020, Xu et al 2022) and specific regions (Tan et al 2020, Wang et al 2020).Han et al (2020) analyzed the drought in China from 1950 to 2009 using the improved gridded Palmer Drought Severity Index (PDSI) (Palmer 1965) and found severe and extreme droughts occur mostly in the Agro-Pastoral Transitional Zone and the Beijing-Tianjin-Hebei Region.However, drought indices only depict drought at a fixed location for a specific period, ignoring the dual nature of drought in space and time (Wang et al 2023).Shao et al (2018) identified drought events using PDSI and the severity-areaduration (IAD) method (Andreadis et al 2005).They found that droughts become more serious across China during 1980-2015.However, drought characteristics calculated by the IAD method depends on the fitness of the IAD curves (Xu et al 2015, 2019, Huang et al 2019).Xu et al (2015) developed a threedimensional method for identifying drought events in the matrix of longitude-latitude-time and applied it to characterizing the drought events across for the 1961-2012 period in China.Drought events identified by this approach are space-time continuous, which is more consistent with reality.Therefore, in this study, we utilized this three-dimensional method to identify drought events and investigate the variations in spatiotemporal characteristics for the 1961-2018 period over the mainland of China at 0.5 • × 0.5 • resolution.In addition to the study of Xu et al (2015), we further conducted an attribution analysis to figure out how the variation of drought events can be attributed to variations of its influencing factors.
Furthermore, while drought is a natural phenomenon, drought disasters are the result of a combination of drought events and adverse social conditions.The risk concept proposed by the Intergovernmental Panel on Climate Change (IPCC) builds a way to figure out to what extent does drought affect the society.Drought risk refers to the adverse impact on a community or system due to the interaction of a hazardous drought event with vulnerable social conditions (IPCC 2014, Carrao et al 2016).Drought risk can be quantified by three components: hazard, exposure, and vulnerability (IPCC 2014, Zhou et al 2023), where hazard refers to the characteristics of drought, exposure is the social and economic elements affected by drought, and vulnerability refers to susceptibility or sensitivity of the socio-economic system to potential hazards and its characteristics that support disaster resilience and adaptation (Carrao et al 2016, Liu andChen 2021).The comprehensive multi-index evaluation method is now widely utilized during drought assessment, where the indices are selected to represent hazard, exposure, and vulnerability considering comprehensiveness, accuracy, and accessibility (Elus Fooladi et al 2021, Sahana et al 2021, Elusma et al 2022).Drought risk assessment studies has been attempted in China for administrative areas and basins in recent years (Chang et al 2016, Guo et al 2021, Li et al 2022), most of which mainly focus on specific regions based on simple drought index series (Dai et al 2020, Hoque et al 2021, Zhou et al 2021).Nevertheless, to the author's knowledge, no risk assessments have been carried out over the whole country based on drought events.
Based on the existing shortcomings, the aims of this study are to (1) investigate and attribute the spatial and temporal variations of the drought characteristics over the mainland of China based on threedimensional events for the 1961-2018 period, and (2) establish an effective drought risk index to assess the latest drought risk for each province-level divisions in the mainland of China.

Study area and data
Meteorological data during 1961-2018 are from the China Meteorological Data Network (http:// data.cma.cn/).Daily precipitation data are from the Dataset of gridded daily precipitation in China (Version 2.0) with a spatial resolution of 0.5 • ×0.5 • .This dataset is spatially interpolated by the thin plate spline method based on the precipitation data from 2472 observation stations in China.Other meteorological data used to calculate the Standardized Precipitation Evapotranspiration Index (SPEI) (including air pressure, air temperature, relative humidity, wind speed, and sunshine time) are gained from the Daily meteorological dataset of basic meteorological elements of China National Surface Weather Station (Version 3.0) and gridded to 0.5 • × 0.5 • by the inverse distance weighting method (Gemmer et al 2004).Soil moisture data with a 0.25 • ×0.25 • resolution during 1961-2018 are from the Global Land Data Assimilation System (GLDAS, https://disc.gsfc.nasa.gov/datasets/) of the National Aeronautics and Space Administration.The GLDAS soil moisture data has a high correlation with the observations and performed well in China (Sun et al 2022).Soil moisture data at 0-100 cm depth are used due to their capacity to reflect drought (Newete et al 2020).All data above are uniformly interpolated to 0.5

Identification method of drought events
We selected the Standardized Precipitation Index (SPI) (McKee et al 1993) and SPEI (Vicente-Serrano et al 2010) with time lags of three and six months.toidentify drought events.The calculation details of SPEI and SPI are supported in text S1.A drought event is a space-time continuum positioned in a three-dimensional longitude-latitude-time matrix.The identification is divided into three steps.Firstly, for each time step, starting from the grid with the lowest SPEI, the 3-by-3 neighborhood grids are checked and added to the drought cluster if their SPEI value is below −1.This procedure is repeated until all the adjacent grids are clustered or there are no compliant grids in the 3-by-3 neighborhood grids of all the grids in the current cluster.In the latter case, another start grid is picked, and then we repeat the procedure above (figure S1(a)).After all the clusters are identified and labeled, the clusters with an area less than the threshold A 0 are deleted.Secondly, the temporal continuity of drought clusters is checked.In the adjacent moments, two clusters can be regarded as one drought event when their overlapping area between them is larger than the threshold A x .Finally, step two is repeated throughout the study period, and all drought events are identified.A 0 and A x are the two parameters in the identification process, which are generally equal.If A 0 and A x is too small, the number of drought events identified will be huge, and the drought duration will be too long to be realistic.On the contrary, few events will be identified, and the drought duration will be too short (Sheffield et al 2009, Haslinger and Bloschl 2017, Poschlod et al 2020).In this study, we set A 0 to 150 000 km 2 as suggested by Xu et al (2019).Then the drought characteristics are calculated as follows.Drought intensity is defined as the mean value of SPEI for all grids in the drought event.Drought area is obtained by cumulating the area of all grids which are spatially nonoverlapping in the drought event.Drought duration is the time interval between the start and end grid in the drought event.

Attribution analysis
As an extension of multiple regression, path analysis is used to estimating the strength and significance of causal connections between variables (Smith et al 1997, Zhang et al 2022).Compare to the commonly used regression methods, path analysis does not require variables to be independent from each other and can decompose the direct and indirect effects of variables on the outcome variable, thus can be employed under confounded situations.
The relative sensitivity of dependent variable y to independent variables xi in the path analysis is named as path coefficient pi, which can be obtained by separating a correlative system with one dependent variable y and multiple independent variables x i (i = 1, 2,…,n): where n is the number of independent variables; R yi is the Pearson correlation coefficient between the independent variables x i and the dependent variable y, representing the total effect of x i on y; P i is the direct path coefficient of x i on y, indicating a direct effect on a path from x i to y; r ij is the Pearson correlation coefficient between the independent variables x i and x j ; r ij P j is the indirect path coefficient from x i to y through x j , denoting an indirect effect x i on y through intermediate x j .
Then the contribution rate of selected factors to the variation is defined as: where CR i is the relative contribution rate for the influencing factor i.

Drought risk formula
Based on the risk assessment framework proposed by IPCC, a drought risk consists of three components: hazard, exposure, and vulnerability (IPCC 2014).Accordingly, equation ( 1) is used for drought risk calculation.
where DRI is the drought risk, the higher the value, the higher the risk.DHI refers to drought hazard, DEI is drought exposure, DVI is drought vulnerability, and wh, we, and wv respectively indicate the weight of DHI, DEI, and DVI.
To quantify DHI, DEI, and DVI, we select indices based on representation, feasibility, and source reliability (see table 1).Drought frequency, severity, area, and duration calculated based on identified drought events are selected as hazard indices.Population density, Gross Domestic Product (GDP) density, and crop acreage are selected to calculate the drought exposure index, considering the impact of drought events on society and the economy.Crop acreage refers to the area in which crops are sown or transplanted, whether cultivated or not.Drought vulnerability indices are age structure (AS) (i.e. the proportion of the population under 14 years old and over 65 years old), output value proportion of agriculture, forestry, husbandry, and fishery (OVR), percentage of effective irrigated area in crop sown area (EIA), soil moisture of 0-100 cm depth layer (SM), the volume of water resources per capita (WR), the volume of water consumption per capita (WC), river network density (RVD), reservoir capacity (RC), and road density (RDD).People in young or old age are weak facing natural disasters, and thus the larger the AS, the larger the DVI.Agriculture, forestry, husbandry, and fishery are industries with high water demand, and thus OVR indicates the impact of drought on the local industrial economy.EIA and SM reflect the resilience of local agricultural systems to drought.WR  2) is used to calculate DHI (or DEI, DVI).The weights of risk indices are determined considering both subjectivity and objectivity, where the Analysis hierarchy process (AHP) is adopted to determine the subjective weights, and the entropy weight coefficient method (EWM) is used to determine the objective weights (Feizi et al 2017, Sahana et al 2021).Details of the normalization and weights calculation for the indices can be found in Text S2.
where D * I refers to DHI, DEI, or DVI, and n is the number of indices.I means the value of each indicator, and w is its weight.

Identified three-dimensional drought events
There are in total 742 drought events identified by the three-dimensional identification method based on SPEI-3 for the 1961-2018 period.The numbers of drought events with different durations are shown in table S1 and the identified drought events over ten months are presented in table S2 in the supplementary information.We also used SPI-3 and SPEI-6 to improve robustness.Long-duration drought events occur most frequently in the 1970s, while more than half of the extremely long-duration events (more than 20 months) are observed in the 1960s.The maximum duration of the identified drought events is 30 months, which does not mean that a region is constantly in drought for 30 months.As drought events spatially migrate, fragment, and reorganize over time, the duration refers to the continuity of drought events as a whole rather than the continuity of drought status in a particular region.Drought event centers are closely distributed in central China, especially in eastern Inner Mongolia, southern Shaanxi, eastern Sichuan, western Hubei, and Guizhou.Another drought center concentration is found in southeast China covering western Zhejiang, Jiangxi, eastern Hunan and Guangdong (figure 1(c)).Drought centers are sparsely distributed in Beijing, Tianjin, Shanxi, Hunan, and Anhui.There are no significant differences in the distribution of drought events within each decade (figure 1(c)).A majority of the drought events have an intensity ranging from −1.2 to −1.6 (figure 1(d)).Extremely intense drought events are mainly distributed in western and northeastern China, including Xinjiang, Tibet, Qinghai, Sichuan, and Inner Mongolia.Besides, in eastern China, Heilongjiang and Zhejiang also suffered several intense drought events.Most drought events affect an area of 500 000 km 2 or less (figure 1(e)).Drought events with vast impact areas are concentrated in western China, including northern Xinjiang, Tibet, and western Qinghai.Shaanxi, Chongqing and Guizhou in central China also reported drought events with large impact areas.The distribution of the affected area and duration of drought events are similar.Western and northern China, including Xinjiang, Tibet, Qinghai, and central Inner Mongolia, experience droughts with longer duration (figure 1(e)).In addition, Inner Mongolia, Shaanxi, Chongqing, and Guizhou also suffered long-duration drought events.Furthermore, decreasing trends in SPEI series from 1961 to 2018 (figure 1(b)) are found in a belt from the northeast to the southwest of China, which implies that these areas are becoming drier and more prone to drought.

Characteristics variations and attribution of drought events
We set up a 10 year moving subset window (Lei et al 2021, Wang et al 2023) to analyze the temporal changes in drought characteristics.The anomalies for intensity, area, and duration all fluctuate above-below the value of 0 during 1961-2018 (figure 2).The intensity and area anomalies prese nt a six-phase pattern of 'negative-positive-negativepositive-negative-positive' while the changes are dramatic for duration anomalies before 1980s.The trends in drought characteristics also share fluctuatral increase-decrease patterns.The intensity of drought events showed a decreasing trend but the affected area and duration showed an increasing trend in each 10 years window after 2007 (figure S4).The positive and negative patterns of the temporal variations of drought characteristics calculated by SPI-3 and SPEI-6 are consistent with that by SPEI-3 despite differences in the magnitude.
We mapped the decadal spatial distribution of the average drought intensity and duration for the 1961-2018 period (figures 3 and S7).High drought intensity grids are mainly located in western China including Xinjiang, Tibet, and eastern Qinghai in the 1960s, and then gradually transfer northeastward to Inner Mongolia, Gansu, western Qinghai, and Sichuan in the 1970s to the 2000s, and finally move southeastward to southern Shaanxi, Henan, Anhui, Jiangxi, and Zhejiang in the 2010s.As for drought duration, long drought duration grids are mainly distributed in Xinjiang and western Tibet in the 1960s and 1970s, while gradually spreading northeastwards to Inner Mongolia, eastern Xinjiang, Ningxia, and western Jilin from the 1980s to the 2010s.This transfer pattern can also be found in spatial drought characteristics identified by SPI-3 and SPEI-6 (figures S5 and S6).
We then investigated how the variation of drought events can be attributed to variations of its influencing factors (i.e.temperature, precipitation, potential evapotranspiration (PET)) in different climate regions in the mainland of China (figure 4).A high consistency occurs in the relative contribution rates to drought events identified by SPEI-3 and SPEI-6.For the entire China's mainland region, the contribution rate of precipitation variations is the largest, accounting for approximately 50%, followed by PET (∼40%) and temperature (∼10%).In the northwest, Qinghai-Tibet Plateau, northeast, and north regions, the contribution of potential evapotranspiration variations to drought intensity variations slightly outweighs that in precipitation.However, in the humid southern regions, the contribution of precipitation far exceeds that of potential evapotranspiration.

Drought risk assessment
In order to investigate impacts of drought on socialecological systems, we assessed the drought risk over mainland China for the 2003-2018 period based on three-dimensional drought events.The spatial distribution of average drought hazard, exposure, vulnerability, and drought risk for the 2003-2018 period is displayed in figure S2.Classification is based on the geometric interval tool in ArcGIS, as geometric interval works best when the data is spread over a large area and is unevenly distributed.Drought risk is mapped for four periods: 2003-2006, 2007-2010,  2011-2014, and 2015-2018 (figure 5).High drought risk values are generally fixed and mainly located in northern China, and most areas in southeastern China are at medium risk.Inner Mongolia reports the highest drought risk, followed by Xinjiang, Gansu, Ningxia, Sichuan, and Heilongjiang.Most provinces were at their highest risk for the period of 2011-2014.Despite being highly hazardous, Qinghai and Tibet are at low risk due to their low exposure and vulnerability (figure S10).
In addition, the temporal change of drought risk for each region from 2003 to 2018 is shown in figure 6. Increasing trends in drought risk are detected in Inner Mongolia, Xinjiang, Sichuan, Henan, Gansu, Hunan, Shanxi, Qinghai.These regions urgently need to develop policy measures to strengthen resilience to drought risk.

Discussion
Based on the 0.5 • × 0.5 • meteorological data, the spatiotemporal variations of SPEI and characteristics of meteorological drought events in the mainland of China during 1961-2018 were analyzed.Then the drought risk was mapped for each provincial region for the 2002-2018 period.
We used the three-dimensional identification method to identify drought events.To justify the reliability of the drought event identification, we compared eight identified drought events with the recorded historical events, including both long and short duration (table S2).The recorded drought events were collected from the China Meteorological Disaster Yearbook.Most of the identified and recorded events are consistent, and the latter shows a shorter duration and smaller area than the former.This discrepancy might be because a drought event was not observed and recorded until it causes adverse social impacts after its emergence (Wang and Yan 2017).
We found that severe, extensive, and long drought events are mainly distributed in western and northern China, which is also reported in previous studies (He et al 2016, Ayantobo et al 2017) while the specific regions of extreme drought events are different.In addition, it is worth noting that the temporal changes in drought characteristics show that the intensity of drought events showed a decreasing trend but the   affected area and duration showed an increasing trend in the last ten years, which is different from previous studies (He et al 2016, Shao et al 2018).That's because we analyzed the drought characteristics from a three-dimensional perspective, which could make more objective and reliable identification of drought events across large areas spanning multiple decades.Furthermore, we found that grids with high drought intensity and long duration tend to move northeastward over the decades.
For the risk assessment, we chose the period 2002-2018 instead of 1961-2018 due to the availability of socioeconomic data.We found that highrisk areas are mainly distributed in northern China, including Inner Mongolia, Xinjiang, Gansu, Ningxia, Sichuan, Hebei, and Heilongjiang.This spatial pattern is generally consistent with the previous studies while some differences exist.For instance, the drought risk in Inner Mongolia is at low risk in the study of Zhao et al (2020) while is at the highest risk in our study.The reason for the disparity may probably due to we investigate drought risk through an event perspective rather than simple drought index.In addition, we utilized subjective-objective combined weights to avoid assigning excessive weights to indicators with high variability (such as GDP and population) and weakening the effects of drought characteristics.Moreover, our study present the risk map on a provincial scale instead of a basin scale (Zhou et al 2021) which can facilitate the implementation of mitigation policies and measures against drought disasters.Furthermore, drought risk for each province is provided every year from 2002 to 2018, and thus the tendencies in risk change can be detected, which reflect the enhanced variability of the process at large time series in the future.
There is subjectivity in both the selection of indices and the calculation of the weight.Different indices or weights may result in diverse and even contradictory risk results.
However, the uncertainty caused by subjectivity can be controlled with the following steps.Firstly, the definitions of drought risk and its three components Secondly, the weight calculation method adopted in this study (AHP-EWM) is an efficient method for complex systems with multi-indices, and the consistency index in AHP ensures its reliability partly (Saha et al 2021).Thirdly, we set the subjective weights of the hazard, exposure, and vulnerability to 0.4, 0.2, and 0.4, respectively, which is generally consistent with previous drought risk studies in China (Wu et al 2017, Ma et al 2022).
Nevertheless, this study has some limitations that can be improved in future research.The threshold of the overlapping area in the threedimensional method can be set as a time-varying parameter according to the area of the overlapped drought clusters.Future drought risk can be predicted with climate models and projected socioeconomic data.Furthermore, the mechanism of variation in drought events can be discussed in future studies.

Conclusions
In this study, we identified three-dimensional drought events and analyzed their spatiotemporal variations based on the 0.5 • × 0.5 • SPEI series over the mainland of China for the 1961-2018 period.Drought risk in 2002-2018 was further assessed based on the drought characteristics and collected socioeconomic data.The key findings are summarized as follows.
(1) Extreme drought events with high intensity, large area, and long duration are mainly located in western and northern China, especially in Inner Mongolia, Xinjiang, Tibet, and Qinghai for the period of 1961-2018.(2) The drought intensity and affected area anomalies present a six-phase pattern of 'negativepositive-negative-positive-negative-positive' .The intensity of drought events showed a decreasing trend but the affected area and duration showed an increasing trend in the last ten years.Over the decades, centers of high drought intensity and long duration tend to move eastward and northeastward, respectively.
(3) The PET variations contributes slightly larger than precipitation variations to drought intensity variations in the arid regions while in the humid southern regions, the contribution of precipitation far exceeds that of potential evapotranspiration.(4) High drought risk areas concentrate in the north of China, including Inner Mongolia, Xinjiang, Gansu, Sichuan, Hebei, and Heilongjiang.Increasing trends in drought risk for the 2002-2018 period are detected in Inner Mongolia, Xinjiang, Sichuan, Henan, Gansu, Hunan, Shanxi, Qinghai.

Figure 1 .
Figure 1.(a) Regions used for drought study in the mainland of China.(b) Spatial distribution of trends in SPEI-3 series from 1961 to 2018, in which dotted grid denotes a significant trend at a 0.05 significance level.(c) Centers (the severest drought grid) of drought events identified by SPEI-3 over the mainland of China in each decade from 1961 to 2018.(d) Intensity of drought events.(e) Affected area of drought events.(f) Duration of drought events.NW, the Northwest; QTP: Qinghai-Tibetan plateau; NE: the Northeast; N: the North; S: the South; HS: Tropical South.

Figure 3 .
Figure 3. Average drought intensity of drought events identified by SPEI-3 in the mainland of China for each decade in 1961-2018.

Figure 4 .
Figure 4. Contribution rate of temperature, precipitation, and potential evapotranspiration to drought intensity during the period of 1961-2018 for different regions in the mainland of China.

Figure 5 .
Figure 5. Distribution of the average drought risk for the period of 2003-2018 in the mainland of China.

Figure 6 .
Figure 6.Temporal change of drought risk for each province in the mainland of China from 2003 to 2018.The black line is the original risk data, and the red line is the linear fit curve.
(i.e.hazard, exposure, and vulnerability) are specific (IPCC 2014, Carrao et al 2016), and the indices such as drought characteristics, population and economy density, irrigated areas, water resources, and water consumption are always considered in risk assessment studies due to their available data (Tan et al 2020, Sahana et al 2021).Then several other indices are added according to the specific study objectives and areas (Ahmadalipour et al 2019, Wang et al 2020).

Table 1 .
Indices for drought risk assessment.
a Output value proportion of agriculture, forestry, husbandry, and fishery.and WC show resistance to water shortage under drought conditions.RVD, RC, and RDD provide water for quick relief and transportation support during drought disasters.RVD and RDD are calculated respectively through dividing the cumulative length of rivers and roads in each region by the region's area.RVD varies far less in 20 years than other indices, and thus we assume that RVD is constant during 2002-2018.Equation (