Cluster analysis of drought variation and its mutation characteristics in Xinjiang province, during 1961–2015

The Xinjiang province of China is vulnerable to drought, but the occurrence of drought varies substantially among different sub-areas. This study investigated drought characteristics in Xinjiang province and its sub-area using the Mann–Kendall trend test, cluster analysis and Morlet wavelet analysis. The results show that drought in Xinjiang is generally becoming less severe, and there is a non-uniform spatial variation of drought, which is especially pronounced for stations in northern Xinjiang. There is a unique spatiotemporal distribution trend of drought in Xinjiang, and the interdecadal variation of drought shows a gradual shift from the east to the west and then back to the east again over the past 55 years. Northern Xinjiang is becoming wetter at a faster rate compared with that of southern Xinjiang, and it also has a higher occurrence of change point sites (70%). The historical drought situation in Xinjiang is better characterized by three clusters. Cluster 1 is the driest, cluster 2 has a clear alleviating tendency of drought, while cluster 3 shows late occurrence of change point. A broader view of the accumulated variation of drought is formulated in this study, which may help to identify potential droughts to support drought disaster management and mitigation. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence (CC BY 4.0), which permits copying, adaptation and redistribution, provided the original work is properly cited (http://creativecommons.org/licenses/by/4.0/). doi: 10.2166/nh.2018.105 om https://iwaponline.com/hr/article-pdf/49/4/1016/537671/nh0491016.pdf 2020 Pei Xie Yuhu Zhang College of Resource Environment & Tourism, Capital Normal University, Beijing 100048, China Xiaohui Lei (corresponding author) Mingna Wang China Institute of Water Resources & Hydropower Research, Beijing 100038, China E-mail: lxh@iwhr.com Ihnsup Han College of Environmental Engineering, University of Seoul, Seoul 130-743, Korea Qiuhua Chen College of Mathematical Sciences, Capital Normal University, Beijing 100048, China


INTRODUCTION
Drought is characterized by a negative water balance originating from a deficiency of precipitation or a lack of available water resources for an extended period of time (Wilhite & Glantz ).It has become an increasingly serious problem with detrimental environmental and socioeconomic consequences.However, drought patterns have become more complicated in recent years due to climate change, and thus there is a need to better understand drought patterns and characteristics.
The spatiotemporal variability of droughts has received considerable attention due to their serious detrimental impacts.The Intergovernmental Panel on Climate Change (IPCC) documented large uncertainties about the 'future vulnerability, exposure, and responses of interlinked human and natural systems' (IPCC ).China's IPCC indicated that the average warming rate in China (0.9-1.5 C) was higher than the global average with an obvious regional difference in the annual precipitation over the last century (http://www.cma.gov.cn).An increase in frequency and severity of drought is expected in the future due to climate changes, and thus the spatiotemporal variability of drought at global and regional scales has become a topic of considerable research interest.Sheffield et al.

Study area and dataset
Xinjiang (73 40 0 -96 18 0 E and 34 25 0 -48 10 0 N) is located in Central Asia with a total area of 1.6 million km 2 and an elevation of À158 m to 7,390 m.It plays an important strategic role in the 'One Belt and One Road Initiative', and shares borders with eight countries: India, Russia, Kazakhstan, Kyrgyzstan, Tajikistan, Pakistan, Mongolia, and Afghanistan (Figure 1).Xinjiang can be geographically divided into two regions by the Tianshan Mountain, one of the seven largest mountains in the world.The extensive development of inland rivers results in the formation of unique 'mountain-oasis-desert' ecosystems in the arid region.Generally, it has a temperate continental climate with limited precipitation.The daily meteorological data collected at 51 meteorological stations from 1 January 1961 to 31 December 2015 were used in this study, and were downloaded from the official Chinese meteorological website (http://data.cma.cn).
The sea surface temperature (SST) data over the North Atlantic Ocean (20-70 N) with a resolution of 5 × 5 were provided by the National Oceanic and Atmospheric Administration (NOAA).Data quality control and homogeneity assessment were attained using the RclimDex software package (Zhang & Yang ).The process consists of two steps: (1) missing records were interpolated using data of nearby stations in the same year; and (2) data quality control was performed and unreasonable data were handled in accordance with the missing data.

Drought indexes
The SPI is a meteorological drought index based solely on precipitation data (Mckee et al. ).Three main advantages may arise from the use of SPI: (1) the calculation is relatively easy as this index is based on precipitation

Proposed methodology
The variation of SPI-12 from the meteorological stations was first examined using k-means analysis, which would enable the grouping of stations with similar temporal trends.The Mann-Kendall (MK) method (Kendall )   The heterogeneity measures (Hosking & Wallis ) shown in Table 1 are used to evaluate the homogeneity of the areas by comparing the dispersion of sample L-moments among sites with the L-moment for the group of sites.The heterogeneity test should follow the following principles: the region is treated as acceptably homogeneous if H < 1; possibly heterogeneous if 1 < H < 2; and definitely heterogeneous if H > 2, respectively.The heterogeneity H statistic and V statistic for the sample and simulated regions can be represented as follows: where u v is the average of simulated V values, σ v is the standard deviation of simulated V values, τ i is the sample L-moment at each site, τ R is the averaged sample L-moment at a regional scale, and n i is the length of the time series at site i, respectively.The H(1), H( 2  widely used in geoscience studies, whose advantage is the simple implementation in the search of clusters.It is a nonhierarchical clustering method which begins with the calculation of the centroids for each cluster, followed by the calculation of the distances between the current data vector and each of the centroids, and finally assigning vectors to the cluster whose centroid is the closest.The iterative steps involved in the K-means clustering include (Sönmez ): (1) All samples are selected randomly into the k clusters, each of which is represented by a centroid.
(2) Computing the centroid of each cluster by averaging its sample vectors.
(3) All samples are redistributed to the nearest cluster according to the distance between the cluster centroid and sample, and then the centroid of the cluster is recalculated.
Steps 2 and 3 are repeated until the clusters become stable.

Cluster analysis
The frequency of droughts at different spatial scales changes, largely depending on geographical locations, basin size, and local hydrological factors.Three main clusters can be obtained using the K-means clustering based on drought, which are largely associated with the topography and climate of the region.The heterogeneity test in Table 1 shows that these three clusters are possibly homogeneous regions.
Figure 3 shows the geographical location of the three clusters (cluster 1, 2, and 3), corresponding roughly to south Xinjiang, north Xinjiang, and mountainous area (Tianshan Mountain, Altai Mountain, and Pamirs), respectively.

Trend analysis of each cluster
Table 2 shows that the maximum and medium SPI-12 values reach a maximum in cluster 3, followed by those in cluster 2 and cluster 1, indicating the high vulnerability of cluster 1 where water scarcity is a tangible constraint.Figure 6 shows an obvious decreasing tendency of drought in all clusters.

Presence of periodicity over time
Mountain have drought change points in some years (detailed in the table).It can be concluded that the most significant change occurs in the 1980s where there is an

CONCLUSIONS
This study investigated drought characteristics in Xinjiang province and its sub-areas using MK test, cluster analysis, and Morlet wavelet analysis.The results show that drought in the Xinjiang area is generally becoming less severe, and there is non-uniform spatial variation of drought, which is especially pronounced in northern Xinjiang.Change point analysis shows multiple change point incidents over the past 55 years.Some salient conclusions can be drawn from this study: (1) There is a unique spatiotemporal distribution trend of drought in Xinjiang, and the inter-decadal variation of drought shows a gradual spatial shift from the east to the west and then back to the east again in the period 1971-2015.
(2) North Xinjiang is becoming wetter at a faster rate compared to south Xinjiang, and it has a higher occurrence of change point sites (70%) than south Xinjiang (30%).
(3) The historical drought situation in Xinjiang is better represented by three clusters rather than a homogeneous region.The periodicity of drought in Xinjiang is stronger in short time scale.Cluster 1 is the driest, cluster 2 has a clear alleviating tendency of drought, and cluster 3 shows late occurrence of change point.

(
) conducted a global assessment of drought under the warming climate over the past 60 years.Numerous regional studies have also been conducted to analyze the spatiotemporal variability of drought (Lewis et al. ; Gosling ).The Xinjiang Uygur Autonomous Region (hereafter referred to as Xinjiang for short) is a key eco-environmental zone in China with a semi-arid climate and the hottest temperature nationwide.Yan et al. () investigated the combined impacts of future climate and land use changes on the streamflow in Xinjiang.Zhang et al. () also investigated the impacts of climate changes on spatiotemporal properties of drought extremes and local agriculture.Zhang et al. (c) found that northern Xinjiang was wetter than southern Xinjiang, and the whole region has exhibited a wetting tendency with a higher frequency of heavy precipitation extremes since 1980.Among the indexes used in monitoring drought (Zhang et al. a; Wang et al. ), the Standardized Precipitation Index (SPI) is suitable for drought reconstruction in Xinjiang (Zhai & Feng ).Previous indexes can be classified into two groups: (1) indexes related to the physical processes of droughts, such as the Palmer Drought Severity Index (Palmer ) and Surface Water Supply Index (Shafer & Dezman ); (2) indexes based only on precipitation, such as Standard Precipitation Index SPI (McKee et al. ).The SPI has been commonly used in recent studies due to its simplicity and temporal flexibility (Li et al. ; Belayneh et al. ).However, the impacts of droughts appear to be multifaceted and often difficult to quantify over large areas and long time scales.Clearly, a better understanding of the spatiotemporal changes in droughts is essential in the development of drought contingency plans (Heim ).This is especially important in Xinjiang with its towering mountains and large low-altitude plateaus or basins.In this study, we investigated the spatiotemporal variation of droughts in Xinjiang and its sub-areas over the past 55 years.We focused on regionalization using a clustering algorithm and drought properties for partitioning meteorology stations of interest.Subsequently, change point analysis was performed for homogeneous regions, and the relationship between SPIbased drought and its affecting factors discussed.The rest of this paper is structured as follows: immediately below, the study area and data set are introduced, as well as the statistical technique used in the study.This is followed by the results for the whole of Xinjiang as well as for different geographic sub-areas.The next section discusses the temporal trend, especially the occurrence of change point in some stations and regions.Finally, the conclusions and recommendations for future research are presented.
alone; (2) it can characterize drought intensity and duration well; and (3) it has a multi-temporal scale application dimension.The SPI-12 is a good indicator of the long-term drought conditions, which is calculated based on the total precipitation amount of the past 12 months.In this paper, the gamma distribution function is found to fit the precipitation data well, because the precipitation does not follow a normal distribution.Detailed computation of the SPI can be found in Cacciamani et al. ().

Figure 1 |
Figure 1 | Location of the study area and the meteorological stations for data collection.
), and H(3) are calculated by the L-coefficient of variation, L-skewness, and L-kurtosis used as the L-moment, respectively.K-means method Different basins and hydrological factors can have different impacts on local water resources and precipitation, and thus the frequency and severity of drought can vary significantly in different sub-areas.The sites of interest are partitioned by the clustering algorithms based on the K-means method Severe drought is observed in north Xinjiang in the period 1971-1980, which might be related to the most severe drought that occurred in 1974.However, further study is needed to fully elucidate the causes of this phenomenon.The inter-decadal variation of drought shows a gradual shift from the east to the west and then back to the east again over a period of 55 years.The most severe drought occurs in the period 1961-1970 and the more recent period 2001-2015 in the east region, whereas the period 1971-2000 shows the reverse phenomenon.

Figure 5
Figure 5(a) shows the inter-annual and inter-decadal variation of drought in the study area based on SPI-12, and Figure 5(b) shows the changing trend of drought obtained by the MK method.Figure 5(a) shows that this region experiences widespread drought from 1961 to the mid-1980s, and

Figure 5
Figure 5(c) shows the changing trends of different drought grades.It shows that the number of sites with 'normal drought' shows an increasing trend (17%) since the early 1990s, whereas that with 'special drought' decreases dramatically and approaches 0% over the last 4 years.The variation tendency of 'normal drought' shows an obvious increasing trend at the rate of 0.33/a, followed by that of 'medium drought', 'mild drought', 'special drought', and 'severe drought' with a rate of À0.09/a, À0.06/a, À0.05/a, and À0.04/a, respectively.These results are largely in agreement with those ofLi et al. (), which also show a decreasing tendency of drought in Xinjiang with additional differentiation of drought grades.

Figure 4 |
Figure 4 | Spatial distribution of drought in different periods (10 years in all plots except for the last one (5 years)).

Figure 7 |
Figure 7 | Dominant periodicities of SPI-12 based drought by Morlet-wavelet analysis in each cluster.

Figure 6 |
Figure 6 | Drought patterns in each cluster according to SPI-12 annual variations.

Figure 8 |
Figure 8 | Spatial patterns of droughts before (a) and after (b) the change point (shown in Figure 5); (c) the significance test represented by Z values.

Figure 9 |
Figure 9 | Change point in each cluster.
thus climate factors, such as sunshine, temperature, and relative humidity, are potential factors affecting the change point.In addition, the variation of global SST patterns and large-scale atmospheric circulation is also associated with regional changes in precipitation and temperature due to tele-connections(Alexander et al. ).Thus, SST is also considered in this study.Correlation analysis was conducted for the early, middle, and latter stages of the change period(1981)(1982)(1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990) and shown in Table4.The results show a significant relationship between precipitation and the SPI-12 value, and an increase in precipitation can result in a reduction in the severity of drought.However, the relationship between drought and relative humidity is not stable, with the maximum value observed in the middle stage.The SPI-12 value is negatively correlated with temperature, drought, and sunshine, probably because an increase in sunshine can result in high temperature and a large amount of evaporation, and consequently the aggravation of drought.However, SST shows a weak relationship probably due to the location of the study area, because Xinjiang is in the hinterland of China, and the moist air from the ocean can be affected by the Tibetan plateau with an average altitude of above 4,000 m.

Table 3
also shows the number of change points in the

Table 3 |
Change-point analysis of the whole of Xinjiang by MK test

Table 4 |
Correlation analysis of drought-related factors during the earlier, middle and latter stage of change period