## 1. Introduction

Drought disasters cause substantial losses of about $6–8 billion worldwide every year (Wilhite 2000). They have a strong influence on global economic development and affect human lives and property. China is one of the most affected countries, and drought has caused large economic losses in its southwest region. This region suffered a severe drought in 2010, which was a once-in-a-century event in some areas. This drought caused billions of dollars in losses and affected more than 60 million people (Yang et al. 2012; Zhang et al. 2012). The spatial patterns and long-term trends of drought occurrence remain unclear. It is particularly important to study temporal variations and spatial patterns of drought at different spatiotemporal scales and to develop appropriate prevention and mitigation plans for drought disasters.

The formation and severity of drought are closely related to meteorological factors, especially precipitation. Observations of precipitation at meteorological stations are typically discrete and sparse in both space and time, however, and hence it is important to determine an accurate regional distribution of annual precipitation through spatiotemporal analysis. Many researchers have focused on methods of spatial interpolation. The methods of Bayesian maximum entropy (BME) and ordinary kriging were used to study spatiotemporal variations of annual precipitation in the Namak Lake watershed area of Iran, and cross validation was used to assess their performance (Bayat et al. 2013). The BME method proved to be better. Shi et al. (2014) used a BME model, with TRMM satellite data as “soft data” and observations from meteorological stations as “hard data,” to estimate precipitation in Fujian Province, China. The cross-validation statistics, mean absolute errors, and root-mean-square errors from the BME, ordinary kriging, and cokriging methods indicated that BME estimates were superior (Shi et al. 2014). Other research has shown that the BME method produced more reliable estimates than did the kriging methods (Christakos and Li 1998; Bayat et al. 2014). Zhang et al. (2016) compared four BME models in mapping annual mean precipitation on the basis of meteorological variables, elevation, and distance to coastline. The BME method has the benefit of considering more information when producing its estimation. The results show that BME produces more reliable estimates by incorporating general and site-specific knowledge, such as physical laws, expert knowledge, and soft and hard data (Modis et al. 2009; Bayat et al. 2013; Shi et al. 2014). Drought severity can be analyzed on the basis of these assessments of regional precipitation distribution.

Drought indicators are important means for measuring drought. The standardized precipitation index (SPI) is based on the cumulative probability of given precipitation at meteorological stations (McKee et al. 1993). Although the SPI does not include evapotranspiration, it is widely accepted worldwide and can be used to analyze different time scales and drought categories (Guttman 1999; Vicente-Serrano et al. 2010; Capra and Scicolone 2012). Guttman (1998) and Hayes et al. (1999) compared the SPI with the Palmer drought severity index and concluded that the SPI had statistical consistency advantages and that it could describe both short-term and long-term drought impacts over various time scales of precipitation anomalies. The SPI is also used in the study of the drought history of a site or region, including magnitude ranking on the basis of analyses of frequency and duration (Sadeghi and Shamseldin 2015; Buttafuoco et al. 2015; Kostopoulou et al. 2017). Thus, the SPI can meet the demand for detecting drought hazard clusters.

Many researchers have studied drought by using statistical methods. For example, interpolation methods have been used to study temporal and spatial distributions (Bayat et al. 2013; Shi et al. 2014; Zhang et al. 2016), the Mann–Kendall method has been applied to study temporal trends (Buric et al. 2015; Ficklin et al. 2015; Verma et al. 2016), and correlation analysis has been used to examine the factors that influence drought hazards (Milošević et al. 2016; Zhang et al. 2016). In addition, Ficklin et al. (2015) used Getis–Ord *I* and Getis–Ord

The study that is presented in this paper applied annual precipitation data from meteorological stations to spatial mapping of precipitation, calculated a drought index, and detected spatiotemporal clusters. We selected Yunnan, Guizhou, and Guangxi as the study area. This area is one of the most drought-afflicted areas in China, with a dense population, high proportion of agricultural land use, and varied weather and terrain. A full procedure is proposed to study drought hazards on the basis of precipitation data. First, annual precipitation data from 90 meteorological stations in or around the study area from 1964 to 2013 were used to determine the regional distribution of precipitation, using a BME spatiotemporal estimation method. Second, an annual-scale SPI was used to attain the regional distribution of drought hazards. Last, the STPSS method was used to detect spatiotemporal clusters of drought hazards for different drought grades. The results may be used to provide support for prevention and mitigation of drought in the study area.

## 2. Study area and data

### a. Study area

The study area is Yunnan and Guizhou Provinces and the Guangxi Zhuang Autonomous Region (Yun-Gui-Guang; 97.31°–112.04°E, 20.54°–29.16°N), which is on the Yunnan–Guizhou Plateau in southwestern mainland China, bordering Vietnam, Laos, Myanmar, and the South China Sea (Fig. 1). The 795 300-km^{2} area includes 39 provincial cities, such as Kunming, Guiyang, and Nanning, which are the capital cities of Yunnan, Guizhou, and Guangxi Provinces, respectively. The study area is the most severely drought-afflicted region of China (Zhang et al. 2013) and is also an important agricultural area; therefore it is highly susceptible to drought. The topography varies greatly in this because of the sharply increasing altitude. The mean terrain elevation is 1000–2000 m. There are approximately 130 million residents in the region, accounting for 9.5% of China’s total population. According to the Statistical Yearbook 2014 (Ma 2015), the gross domestic product in the study area only amounts to 6% of China’s total.

The region has a subtropical monsoon climate. Drought is common in spring because of sparse rainfall and strong evaporation. Agricultural losses caused by drought in the study area amount to 10.6% of total agricultural losses caused by drought in China. Moreover, the drought losses amount to 43.6% of the total meteorological agricultural losses in the study area. The Yun-Gui-Guang region is also one of the most severe drought centers in China. We select this study area to analyze the spatiotemporal characteristics and spatiotemporal clusters of drought.

### b. Data

The data used in this study were acquired from China’s annual terrestrial climate dataset, which were published by the China Meteorological Data Sharing Service System (Zou and Zhu 2008). We used 50 years (1964–2013) of annual precipitation data to examine the spatiotemporal distribution of precipitation from 90 meteorological stations in or around the study area (Fig. 1). There were some null records at 18 stations, which were replaced by the value −32 766. These stations were called soft-data meteorological stations, and the other 72 were called hard-data stations.

The historic rainfall data of the soft-data stations were fitted to a gamma distribution, because the gamma distribution has been found to fit the precipitation distribution well (Watterson and Dix 2003; Husak et al. 2007). In this work, the soft data were fitted using the nonlinear least squares method that was based on the precipitation datasets from soft-data stations with a 95% confidence level. The precipitation distribution functions of all soft-data stations were obtained. Data for the unrecorded years were then estimated by using MATLAB R2010b software and a Gaussian kernel density-estimation method that was based on mean values and variances. These estimated values were in the form of probability density functions (PDF). The soft data that were in the form of PDFs were used as replacements for the missing data. The hard data were analyzed in their pure form.

Figure 2 shows the detailed data-preprocessing procedure. After the BME spatiotemporal estimation, we determined the regional distribution of annual precipitation. Then, regions of near-normal, moderate, severe, and extreme drought were identified on the basis of the annual-scale SPI. The drought hazard grades and category-classification system that are based on SPI are shown in Table 1.

Drought hazard grades and category-classification system, as based on SPI (Zhang et al. 2006).

## 3. Methods

### a. Workflow

The workflow of the method applied in this study is composed of gathering and preprocessing of annual precipitation data, estimation of logarithmic (log) annual precipitation, and spatiotemporal distribution along with analysis of the most likely clusters of drought hazards, as shown in Fig. 3. The process of data gathering and preprocessing has already been introduced in section 2b, and the several other methods that are involved in our study are explained in detail in sections 3b–3d.

### b. Spatiotemporal random-field model

The records of annual precipitation are spatiotemporal data (a time series for each meteorological station); therefore, precipitation is considered to be a spatiotemporal random field [S/TRF; *X*(**p**)] in this study (Modis et al. 2009), where **p** = (**s**, *t*), **s** is the spatial position vector, and *t* denotes time (e.g., 1 year). Herein, we use uppercase English letters [e.g., *X*(**p**)] to denote random fields, lowercase English letters (e.g., *x*) to denote random variables, and lowercase Greek letters (e.g., *χ*) to denote their realizations. For example, the vector *χ*_{data} = (*χ*_{1}, …, *χ*_{m}) denotes the annual precipitation observations available at points *p*_{i} (*i* = 1, …, *m*). To simplify the calculation, the log function was used to process the raw precipitation data *χ*_{data} [=(*χ*_{hard}, *χ*_{soft})]. Log annual precipitation Ln*X*(**p**) can be obtained from the log function for *X*(**p**). The term Ln*X*(**p**) can be decomposed into Ln*X*(**p**) = *R*(**p**), where *R*(**p**) indicates a residual precipitation component that is homogenous in space and stationary in time, with a zero mean. The mean trend *m*_{s}(**s**) + *m*_{t}(*t*) (Nunes and Soares 2004), where *m*_{s}(**s**) is the purely spatial component, obtained by averaging Ln*X*(**p**) values of every spatial site and then applying a spatial exponential smoothing function to remove local fluctuations, and *m*_{t}(*t*) is the purely temporal component, obtained by applying a temporal exponential smoothing function to Ln*X*(**p**) values for each year (Christakos et al. 2001).

*c*

_{x}(

*r*,

*τ*) (Christakos et al. 2001; Heuvelink and Griffith 2010; Christakos et al. 2012) aswhere

*r*= |

**s**−

**s**

_{1}| and

*τ*= |

*t*−

*t*

_{1}|. The covariance function

*c*

_{x}(

*r*,

*τ*) is a second-order statistical moment that describes Ln

*X*(

**p**) variability in space and time. The covariance function can be taken as a purely spatial function when

*τ*= 0, and as a purely temporal function when

*r*= 0.

We conducted spatiotemporal covariance analysis of log annual precipitation in the MATLAB R2010b software environment by using the BMElib toolbox (http://www.unc.edu/depts/case/BMELIB/), which implements a collection of space–time geostatistical methods that include both classical kriging-based techniques and modern techniques that are based on BME theory (Kulldorff 2015).

### c. Bayesian maximum entropy

Christakos established the BME method in 1990 (Christakos 1990). Spatiotemporal estimation on the basis of BME is now widely used in some fields for spatiotemporal analysis and mapping (Christakos and Serre 2000; Yu et al. 2009). It uses many types of data and various types of physical knowledge bases for spatiotemporal estimation. These knowledge bases are separated into general knowledge base *K*_{G} and site-specific knowledge base *K*_{S} (Douaik et al. 2005). In this study, *K*_{G} characterizes the global characteristics of the annual precipitation S/TRF, such as its mean trend and its spatiotemporal covariance, and *K*_{S} consists of the soft and hard data of annual precipitation. There are three stages to BME spatiotemporal estimation, as presented in Fig. 4.

The aim of the *prior stage* is to determine the PDF of log annual precipitation on the basis of *K*_{G}, called the prior PDF *f*_{G}(*χ*_{map}). In this stage, basic statistical constraint conditions in *K*_{G}, which contain means and covariance functions of log annual precipitation, are considered in computing *f*_{G}(*χ*_{map}). Details of computing *f*_{G}(*χ*_{map}) are given in the appendix.

The objective of the *preposterior stage* is to collect and organize additional auxiliary information in appropriate forms to produce site-specific knowledge *K*_{S} (Christakos 1998). The integration and processing of physical knowledge base *K* = *K*_{G} ∪ *K*_{S} of annual precipitation are used in the BME estimation. Hard data are incorporated in the prior stage indirectly and are used directly in the preposterior stage.

*posterior stage*is to update the prior PDF on the basis of the Bayesian conditional probability theorem and

*K*, thereby attaining the posterior PDF

*f*

_{K}(

*χ*_{k}). The soft data of log annual precipitation are in the form of a PDF, and the hard data are certain, and therefore the posterior PDF

*f*

_{K}(

*χ*_{k}) at unmeasured location

**p**

_{k}(

*k*≠

*i*) iswhere

*f*

_{S}(

*χ*_{soft}) is the PDF of the soft data.

The BME spatiotemporal estimation of precipitation was executed using the BME graphical user interface (BMEGUI) 3.0 (http://www.unc.edu/depts/case/BMEGUI/) free software. The complete datasets of hard and soft data, the spatiotemporal covariance model, and the covariance parameters were taken as input parameters. The system parameters of BMEGUI 3.0 were set as shown in Table 2.

System parameters of BMEGUI 3.0 to estimate regional spatiotemporal log precipitation in the study area.

The annual-scale SPI was used to estimate drought severity according to the China Meteorological Drought Classification Standard GB/T20481-2006 (Zhang et al. 2006), on the basis of the estimated annual precipitation data. In this standard, the applied SPI algorithm is a modification of the well-known SPI so as to be more applicable to China. The necessary parameters have been provided, which were fitted using Chinese historical rainfall data. The annual-scale SPI could be calculated by applying annual precipitation data to the algorithm and the historical parameters. The algorithm was coded and executed in the MATLAB R2010b software to calculate SPI.

### d. Space–time scan statistic

The scan statistics can be divided into three aspects: spatial (Kulldorff and Nagarwalla 1995), temporal (Naus 1965), and space–time (Kulldorff et al. 1998). STPSS is one of the methods that use space–time scan statistics and is used to identify clusters of space–time interaction within patterns of spatiotemporal events.

The STPSS model imposes a cylindrical window in the study area. The base of the cylinder represents space, whereas the height represents time. The cylinder is flexible in its geographical base and in its starting time, which are independent of each other (Wang et al. 2015). The center of the cylinder is then allowed to move across the study area and period so that the cylinder contains different sets of drought hazard cases at different positions and periods (Kulldorff 2001). Using all drought hazard cases in the study, the STPSS model tests the null hypothesis (complete spatial randomness) against the alternative hypothesis, namely, that the probability of a case being inside the zone is greater than that of it being outside the zone. The STPSS model is suitable to test this hypothesis because it is likelihood based and thus the most likely zones can be selected and tested for statistical significance (Onozuka and Hagihara 2007). The processes of this model are as follows:

*z*there are

*n*

_{z,t}drought hazard cases during year

*t*. The total number of drought hazard cases

*N*in the study area and period isThus, the expected number of drought hazard cases

*A*is the sum of these expectations over the study area and years within the cylinder. The equation is

*z*, given that it was observed in

*t*, is for all years. If we let

*n*

_{A}be the observed number of drought hazard cases in

*A*, then

*n*

_{A}obeys a hypergeometric distribution, and it is a discrete probability distribution. The mean is

*N*is very large when compared with both

*n*

_{A}can be taken as an approximate Poisson distribution with mean

*A*using the Poisson generalized likelihood ratio on the basis of that approximation. The equation is as follows (Malizia 2013; Wang et al. 2015):Monte Carlo hypothesis testing (Dwass 1957) is used to evaluate statistical significance for the most likely clusters of drought hazards, and the significance value

*p*is also calculated.

The spatiotemporal clusters detection was calculated using SaTScan (http://www.satscan.org/), which is free software developed by M. Kulldorff (Kulldorff 2015). The space–time analysis is partitioned into two types: retrospective and prospective. We selected the retrospective analysis to detect drought clusters of past years in this study. There were a total of 1990 estimated coordinate points in the study area; every estimated coordinate point was a 50-yr sequence of drought hazard cases. There were 14 541, 11 692, 7602, and 5201 drought hazard cases of near-normal, moderate, severe, and extreme drought, respectively, over 50 yr. The input data contained geographical coordinates and estimation-drought-point event datasets. The maximum allowable spatial and temporal clusters sizes were 50% of the study area and period. The number of simulated Monte Carlo replications was set to 999 to ensure an excellent power. Statistical significance of the *p* value was set to 5%. The output of every cluster contained a period, the ratio of observed to expected cases, a test statistic, a *p* value, and a shapefile.

## 4. Results and discussion

### a. Spatiotemporal covariance analysis

Marginal experimental covariance values and fitted models in space and time of log annual precipitation are shown in Fig. 5. Figure 5a is a purely spatial covariance function, and Fig. 5b is a purely temporal covariance function.

The fitted spatiotemporal covariance model of log annual precipitation is shown in Fig. 6. The model provided a more accurate representation of the correlation structure of annual precipitation in both space and time than that described by a purely spatial covariance model or a covariance model in which time was taken as an additional spatial coordinate (Douaik et al. 2004).

*a*

_{1}= 0.268,

*a*

_{2}= 1.1°,

*a*

_{3}= 3 yr,

*a*

_{4}= 0.055,

*a*

_{5}= 4.5°, and

*a*

_{6}= 100 yr. The

*R*

^{2}of the fitted covariance was 0.928, which means that the model did a good job of explaining the log annual precipitation values. The first covariance component served to model the small-scale structure of fluctuations in space and time of log annual precipitation, whereas the second component modeled the large-scale structure of the fluctuations of log annual precipitation.

### b. Spatiotemporal distribution of drought hazards

The regional precipitation distribution was estimated for every year for the period of 1964–2013. The estimation results were probabilistic soft data containing the means and variances, which were in the form of a Gaussian distribution. Figure 7 shows results for three estimation points near the capital cities (Kunming, Guiyang, and Nanning) and four arbitrary years (1968, 1980, 2000, and 2010). Then, the estimated results were transformed using a natural exponential function, yielding regional precipitation mapping. Annual precipitation distribution images were mapped in the ArcGIS 10.2.2 software. Figure 8 shows the maps produced for the four arbitrary years.

Figure 7 reveals more rainfall in Nanning than in Guiyang or Kunming. Probability densities of precipitation were larger in Kunming and Guiyang than in Nanning, and widths of the log precipitation Gaussian distribution were smaller than in Nanning, indicating that the variance in Nanning was larger than in the others. In addition, the spaces between curves of Nanning were much larger. Therefore, it was evident that there were more fluctuations in Nanning than in Kunming or Guiyang. Overall, there was more rain in the south and southeast because these regions were adjacent to the South China Sea, and there was little rain in the northwest because it was located well within the interior of China. In addition, there was more rain in the south than in the north of the study area and more in the east than in the west.

Figure 8 showed that the precipitation in Yunnan Province was relatively low, especially in the northwest and middle areas. The southern part of Yunnan Province had higher precipitation. The precipitation fluctuated greatly in Guizhou Province. On the whole, there was a trend of higher precipitation in the southern part and lower precipitation in the northern part of Guizhou Province. Guangxi Zhuang Autonomous Region had abundant rainfall, but there was less precipitation in some years in the southern part.

Drought hazards were assigned four grades on the basis of SPI: near-normal, moderate, severe, and extreme (Table 1). Graded hazards were regionalized for the four arbitrary years (1968, 1980, 2000, and 2010) in ArcGIS 10.2.2 (Fig. 9). Extreme drought was mainly concentrated in the northwestern and middle parts of Yunnan Province, and severe drought was mainly concentrated in the southeastern and middle parts of Yunnan Province and the northwestern part of Guizhou Province (Fig. 9). Moderate drought was distributed in most of Yunnan Province, the northwestern part of Guizhou Province, and the southwestern part of Guangxi Zhuang Autonomous Region. This result indicated that Yunnan Province was a drought-prone area, especially in its northwest and center, where there was extreme drought. The next-most drought-prone area was Guizhou Province.

From the annual SPI spatiotemporal mapping, we determined the frequencies of each drought grade at every estimation point. The drought-frequency map is shown in Fig. 10. Some areas suffered drought nearly every year, as highlighted by northern and central Yunnan Province. Near-normal and moderate drought were likely throughout the study region, with Yunnan and Guizhou Provinces the most likely to suffer drought. Severe and extreme drought concentrated in Yunnan Province, with high frequency. Overall, there was a decreasing trend of drought frequency with increasing drought severity and a northwest–southeast trend in frequency. The total areas affected by drought and the percentages of areas affected by each drought grade were calculated (Fig. 11). Figure 11 shows that the area affected by drought was about 30%–45% of the total area every year, with an irregular period of approximately 17 yr. The histograms also showed a weak increasing trend in total drought. This trend and the various frequencies were probably caused by differences in geology, climate, and level of human activity.

On the one hand, the annual precipitation and drought may be influenced by topography, elevation, and distance from the ocean (Zhang et al. 2016). The Guangxi Zhuang Autonomous Region, with lower elevation and close proximity to the ocean, has higher precipitation and is thus less affected by drought. In contrast, Yunnan Province is located in the Yunnan–Guizhou Plateau, distant from the ocean, and therefore it is subject to low precipitation and thus is susceptible to drought. On the other hand, the annual precipitation has changed with the changing global climate and the increased urbanization of the study area.

### c. Most likely clusters of drought hazard

Retrospective space–time scan statistics indicate that there were 9, 7, 9, and 6 most likely spatiotemporal clusters detected for near-normal, moderate, severe, and extreme drought, respectively (Table 3). These clusters were part of the study area in different years. The cluster period contained all study years, and 1966 had the most frequent clustering of five times: Cluster 5 of moderate drought; clusters 1, 5, and 8 of severe drought; and cluster 1 of extreme drought. The ratio of observed to expected cases showed considerable fluctuations, from 1.48 to 31.15. The *p* values of all calculated clusters were less than 0.001. Larger test statistics of a cluster indicated that it had a higher significance level.

Summary and test statistics of spatiotemporal clusters of events with various drought severities from retrospective analysis using a space–time permutation model in the SaTScan V9.4.2 software.

Figure 12 shows spatiotemporal cluster distributions of each drought grade and the points used to estimate the drought events contained within the clusters. The nine clusters and cases contained in the near-normal drought are shown by green and gray dots in Fig. 12a. The cluster extent in space was very large, with an area of 465 193.4 km^{2}, or 58.51% of the total study area. These clusters covered the study area homogeneously. The period length was 35 yr, with 13 years clustered twice, that is, 1969–72, 1981–84, 1989, and 1998–2001. Cluster 9 had the longest period, at 17 yr (1967–84). Cluster 3 followed with 10 yr (1981–90), and its spatial extent was the largest, covering southeastern Guizhou and northeastern Guangxi.

The seven clusters and cases within the moderate drought were shown by dots with hues of yellow and gray in Fig. 12b. Cluster extent was relatively large, with an area of 375 251 km^{2}, or 47.18% of the total study area. These clusters covered central Yunnan, southern Guizhou and northern Guangxi. The period of these clusters was 34 yr, with only three years clustered twice (1972, 2002, and 2003). Cluster 5 had the longest period, 19 yr (1965–84), and covers western Yunnan.

The nine clusters and cases categorized as severe drought are shown by dots with hues of light red and gray in Fig. 12c. The area of these clusters was 362 515.5 km^{2}, or 45.58% of the total study area. These clusters covered all of Yunnan and Guizhou homogeneously and only a small part of Guangxi. Their period was 39 yr, the longest of the four drought grades, with 16 years clustered twice (1964–77, 1979, and 1980) and 1 year (1966) clustered three times. Cluster 8 had the longest period, 21 yr (1966–86), but its spatial extent was relatively small. Cluster 4 had a long period of 15 yr (1997–2011). Clusters 3 and 1 had relatively large extents, covering western Yunnan and northeastern Guizhou.

The six clusters and cases contained by extreme drought are shown by red and gray dots in Fig. 12d. The area of these clusters was 316 153.7 km^{2}, or 39.75% of the entire study area. These clusters covered central Yunnan and the northernmost part of Guizhou. Their period was 26 yr, and no years were clustered twice. Cluster 3 had the longest period, 12 yr (1996–2007), with a relatively small spatial extent. Clusters 2 and 1 had relatively large extents, covering southwestern Yunnan and northern Guizhou.

Overall, near-normal and moderate drought covered nearly all of the study area. Severe and extreme droughts were concentrated on Yunnan and Guizhou Provinces. These results and historical records were consistent. The period of the clusters varied from 1964 to 2013, covering all study years. Some years were clustered two times or more. Such variation is likely caused by climate change and topography. In terms of natural causes, the study area is inland, and the high Tibetan Plateau and Himalaya form a barrier that makes it difficult for moisture from the Indian Ocean to reach it. Furthermore, the southwest monsoon arrives late and the precipitation period is delayed. Human activities are also likely to contribute to this variation (e.g., population increase, industrial and agricultural development, inappropriate land-use choice, reduction of vegetation cover, and variation in water conservation measures).

## 5. Conclusions

In this study, BME spatiotemporal estimation and the annual SPI were used to map the spatiotemporal distribution of annual precipitation and to regionalize grades of drought hazards in the study area, respectively. The method of space–time scan statistics was then used to detect spatiotemporal clusters of drought hazards for various drought grades. The results are summarized as follows:

- There was more rain in the south and southeast, which are adjacent to the South China Sea. There was little rain in the northwest, which is in the interior of China. There was also more rain in the south than in the north of the study area, and rain was concentrated more in the east than in the west. Yunnan Province was a drought-prone area, especially in its northwest and center, where there was mostly extreme drought. The next-most drought-prone area was Guizhou Province.
- The entire study area had clusters of near-normal and moderate drought. Yunnan and Guizhou Provinces were high-cluster areas of severe and extreme drought. The year 1966 was the most likely cluster year; it was clustered five times. Of these clusters, one was of moderate drought, three were of severe drought, and one was of extreme drought.

These results provide a valuable reference for disaster-prevention and drought-mitigation activities in the study area such as optimization of the distribution of drought-resisting resources, drought monitoring, and evaluation of drought impacts. Measures should be taken in the Yun-Gui-Guang region, such as increased publishing of warning information for drought and the development of contingency plans. There should also be some changes to human activities; for example, we can build water-conservancy projects to address the problem of uneven rainfall-season distribution and can plant trees to enhance forest cover, water, and soil conservation. Moreover, it is necessary to improve emergency preparedness, mitigation, and response capabilities in the area, especially in Yunnan and Guizhou Provinces.

Future research could focus on improvements to the approaches used in this study. More covariates, for example, elevation and land type, can be used in BME estimation to obtain more accurate results. It may be helpful to take additional parameters into consideration for further drought hazard analysis. Considering the inhomogeneous background under which drought occurs, the method of space–time scan statistics can be extended using an arbitrary distribution [not necessarily a complete spatial random distribution, which means that points are generated according to the homogeneous binomial point process (Okabe and Sugihara 2012)] as the null hypothesis.

The authors acknowledge support from the National Natural Science Foundation of China (Study on Pre-qualification Theory and Method for Influences of Disastrous Meteorological Events; Grant 91224004) and Project in the National Science and Technology Pillar Program during the Twelfth Five-year Plan Period (Development Planning of Emergency Management Mechanism and Emergency Plan Hierarchy System of Towns; Grant 2015BAK10B01). We also appreciate support for this paper from the Collaborative Innovation Center of Public Safety.

# APPENDIX

## Details on Computing the Prior PDF

*x*

_{map}is log annual precipitation in the study area and

*χ*_{map}= (

*χ*_{hard},

*χ*_{soft},

*χ*_{k}), with

*k*≠

*i*; components

*χ*_{hard},

*χ*_{soft}, and

*χ*_{k}indicate values of hard data, soft data, and location for estimation, respectively. Thus, the expected information entropy of log annual precipitation is defined as

*g*

_{α}are the given functions from

*K*

_{G}. The

*g*

_{α}functions are taken account of in full in the estimated process, and their expectations

*E*(

*g*

_{α}) provide the space–time statistical moments of interest (Douaik et al. 2005). According to

*K*

_{G}, the statistical constraint conditions of log annual precipitation are given bywhere

*g*

_{α}(

*χ*_{map}) are the known functions associated with

*χ*_{map}on the basis of

*K*

_{G}, including the covariance models

*c*

_{x}(

*r*,

*τ*), and

*N*

_{c}is the number of conditions. On the basis of these constraints and the Lagrange multipliers, the prior PDF is obtained:where

*μ*

_{α}indicates Lagrange multipliers and

*A*indicates a normalization coefficient:

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