1 Introduction

Droughts, which occur frequently and account for a large part of the losses suffered through meteorological disasters worldwide, consistently attract a great deal of attention amongst the scientific community and public alike. Thus, drought indices have emerged as a hot topic in meteorological research. Meteorological drought indices differ from one another in terms of applying different data and different calculation methods. Common meteorological drought indices include PAP (precipitation anomaly percentage), SPI (standardized precipitation index),K-index,Z-index, and PDSI (Palmer drought severity index) (Zou et al., 2005), and studies on the characteristics of drought have been carried out for some regions by using these indices (Dai et al., 1998;Szinell et al., 1998;Bonaccorso et al., 2003;Wei, 2004;Wang et al., 2005;Brázdil et al., 2009;Kasei et al., 2010). Meanwhile, a number of studies (Yuan and Zhou, 2004;Han et al., 2009;Wang et al., 2013) have compared applications of different drought indices in different regions, so as to identify suitable drought indices for particular areas. Drought is a recurring and complex extreme phenomenon that can be categorized into four types: meteorological, agricultural, hydrological, and socioeconomic (American Meteorological Society, 1997). To date, even within a particular one of these categories, a “perfect” drought index that can be widely accepted and applied across the globe has yet to be identified.

Zhang et al. (2006) developed the composite-drought index (CI), which is based on the SPI, the relative moisture index (Cao et al., 2013), and the cumulative effect of precipitation and the impact of evapotranspiration. The CI has been applied in drought monitoring and assessment at the Beijing Climate Center and, during this time, much research on the index (Zou and Zhang, 2008;Zou et al., 2010;Zhao et al., 2011;Zhang et al., 2012) has been carried out. Meanwhile,Lu (2009) developed an index named the weighted average of precipitation (WAP), which takes into account the new concept of “effective precipitation” (Byun and Wilhite, 1999) by using the daily-weighted-average precipitation to characterize the current drought/flood status. However, WAP only considers the quantity of precipitation; it cannot reflect regional and seasonal differences to produce a unified standard to define drought. To overcome this shortcoming,Zhao et al. (2013) developed a new version of the index and named it IWAP (improved WAP).

It is well-known that meteorological drought is gene-rally a regional event, which means it involves a particular area and duration.Dracup et al. (1980) analyzed drought occurrence over global land areas for the period 1950–2000 by applying a drought index based on percentile soil moisture values relative to the 50-yr climatology. Based on gridded precipitation and temperature data and a physics-based macroscale hydrological model,Andreadis et al. (2005) presented the 20th century droughts in the conterminous United States characterized by their severity, frequency and duration, and areal extent.Qian et al. (2011) constructed a daily composite-drought index using station daily precipitation and temperature, and then analyzed the spatiotemporal variations of the site and regional droughts in China during 1960–2009. Recently, the objective identification technique for regional extreme events (OITREE) was developed (Ren et al., 2012), and has been applied in regional drought analyses (An et al., 2014;Li et al., 2014).

In the present study, we employed OITREE to detect regional drought events in China based on CI and IWAP, and compared their results, aiming to discover which of the two indices has the greater potential for daily drought monitoring.

2 Data and method 2.1 Data

The daily precipitation data of 723 meteorological stations in China, for the period 1961–2010, supplied by the National Meteorological Information Center of China, which have been homogenized (Yang and Li, 2014), were used in this study. A simple data quantify-check procedure, which eliminated the stations with a ratio of missing data above 5%, was adopted. Following this, 577 stations were retained for calculating the IWAP in this study.

The daily CI dataset provided by the National Climate Center, China Meteorological Administration was used. This dataset contains the daily data of 577 meteorological stations in China from 1 January 1961 to 31 December 2010.

2.2 Methods 2.2.1 CI

The CI was developed by Zhang et al. (2006), and is constructed based on the SPI of the last 30 days (monthly scale), the SPI of the last 90 days (seasonal scale), and the relative moisture index of the last 30 days. The formula is as follows:

$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\hspace{-87pt} {\rm{CI}} = 0.4{Z\!_{30}} + 0.4{Z\!_{90}} + 0.8{M\!_{30}}, $

(1)

$\,\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\; {M\!_{30}} = \frac{{{P_{30}} - {{{\mathop{\rm P\!E}\nolimits} }_{30}}}}{{{{{\mathop{\rm P\!E}\nolimits} }_{30}}}},\hspace{200pt} $

(2)

where Z₃₀ and Z₉₀ are the SPI of the last 30 and 90 days, respectively;M₃₀ is the relative moisture index of the last 30 days;P₃₀ is the precipitation of the last 30 days; and PE₃₀ is the potential evapotranspiration of the last 30 days.

2.2.2 IWAP

The IWAP was developed by Zhao et al. (2013). A brief introduction to the calculation method is provided as follows.

Firstly, the daily WAP (Lu, 2009) is calculated as

$ {\rm{WAP}} = (1 - a)\sum\limits_{n = 0}^N {{a^n}{P_n}} , $

(3)

where N and P_n are the maximum number of days ahead of the current day and the precipitation n days ahead of the current day, respectively; and the value of a is suggested to be close to 1.0. Equation (3) shows that the WAP may reflect the impact of pre-precipitation and precipitation on the current drought/flood status, and the contribution of pre-precipitation to this status decreases exponentially.

Then, the IWAP is constructed by the following two steps.

(1) Determine the values of the parameters N and a in Eq. (3).Zhao et al. (2013) suggested that they should take values of 150 day and 0.97, respectively.

(2) Remove regional and seasonal differences by nondimensionalizing WAP as follows:

$ {\rm{IWAP}} = c \times \frac{{({\rm{WAP}} - \overline {{\rm{WAP}}} )}}{{\overline {{\rm{WAP}}} }}, $

(4)

$ c = \left\{ \begin{array}{l} 1\;\;\;\;\;\;\;\;\;& ({\rm{pr}} > 300)\\ 0.02\;\;\;& ({\rm{pr}} \leqslant 300) \end{array} \right., $

(5)

where ${\overline {{\rm{WAP}}} }$ is the climatological average of WAP for the period 1961–2010,c is a regional control coefficient, and pr is annual average precipitation in mm.

2.2.3 OITREE method

Based on the CI and IWAP, the OITREE method was employed to identify China's regional drought events (CRMDEs). A detailed description of the OITREE method can be found in Ren et al. (2012).

According to the suggestions for setting values for the parameters in the OITREE method by Ren et al. (2012),Table 1 provides the values of the parameters for the CRMDEs based on the CI and IWAP.

(1) Threshold for the daily drought index: Drought occurs at individual stations when CI (IWAP) ≤ –1.2 (–0.5).

(2) Threshold for the neighbor station distance: For a certain station, all stations within 250 km of it are defined as its neighbor stations.

(3) Threshold for the number of drought stations in a belt: If the number of drought stations in a belt is not smaller than 20, the belt is defined as a drought belt.

(4) Threshold for the ratio of overlapping stations for a daily drought belt: If the ratio of overlapping stations for a drought belt on a certain day to the affected area of an ongoing event on the day before is above or equal to 0.6, the drought belt belongs to the ongoing event.

(5) Threshold for the number of days for a gap in an event: The threshold is set to be 0 day, which means no gap is allowed in an event.

(6) Index and its threshold for defining a regional event as a CRMDE: The integrated index Z (suppose Z_CI and Z_IWAP are based on CI and IWAP, respectively) and the threshold are determined. A regional event can be defined as a CRMDE when Z_CI > 0.7 (Z_IWAP > 0.2). Accordingly, 174 and 184 CRMDEs were identified based on CI and IWAP, respectively.

(7) Thresholds for classifying the CRMDEs: According to the distribution of the integrated index Z, the CRMDEs can be divided into extreme (10%), severe (20%), moderate (40%), and slight (30%) events. Accordingly, the thresholds of the integrated index Z for classifying the CRMDEs, i.e.,Z_CI (Z_IWAP), were easily determined as 3.9 (4.9), 1.8 (2.7), and 0.7 (0.6), respectively.

3 Results 3.1 Comparison of extreme drought events

According to the classification standards of drought events in Table 1, there were 17 and 18 extreme drought events during 1961–2010, based on CI and IWAP respectively.Table 2 lists these extreme events. Comparison between the two results shows the following three promi-nent features.

(1) Ten events (highlighted in bold font in Table 2) were identified as extreme events in both sets of results. In addition, amongst the remaining 7 CI extreme events, 6 were identified as severe events and 1 was divided into a severe event and a moderate event in IWAP's results, while the remaining 8 IWAP extreme events were all identified as severe events in CI's results.

(2) The 2 events that showed good consistency were the 1998/99 North China drought event and the 2009/10 Southwest China drought event. The former ranked No. 1 in both sets of results, but there was a difference between the start and end times of about half a month, respectively. The latter ranked No. 4 in CI's results and No. 3 in IWAP's, and there was a difference in the start and end times of about 20 days between the two sets of results.

(3) For the 10 common extreme events, the 2 events with the largest differences in start and end times were as follows: the No. 3 CI event ended 63 days later than the corresponding IWAP event (No. 11), and the No. 2 IWAP event started 54 days earlier than the corresponding CI event (No. 16).

Further comparison between the above results and previous studies (Ding, 2008;Zhang et al., 2009) revealed that some of the most severe drought events on record, such as the 1998/99 North China drought event, the 2009/10 Southwest China drought event, the 1962 spring/summer northern China drought event, and the 1965 spring/summer North China drought event, were all identified as extreme events in both sets of results, i.e., those based on CI and those based on IWAP. The above analysis indicates that both CI and IWAP have strong ability in identifying regional extreme drought events.

In order to analyze the characteristics of drought based on the two indices, the 1998/99 North China drought event, which was ranked No. 1, was chosen for further comparison.Figure 1 presents the distribution of accumulated intensity for this drought event based on CI and IWAP, separately. As we can see, the scope of influence and intensity distribution of the event based on the two indices were highly consistent, with a correlation coefficient between them of 0.87. The drought event affected most of central–eastern China, with the most serious drought region occurring in North China and eastern Northwest China.

The variations of daily CI, IWAP, and precipitation over Taiyuan, which was located at the center of the drought event, indicated that, based on IWAP, the drought process started in early November 1998 and then developed slowly before entering the most severe stage around 19 February 1999, within a case of non-precipitation from 20 December 1998 to 19 March 1999 (Fig. 2). Whilst this seems a reasonable result, the drought process based on CI showed two unreasonable phenomena: (1) under non-drought conditions, a severe drought stage suddenly occurred in mid November; and (2) drought alleviated gradually from 8 December to 22 January in the case of non-precipitation.

Figure 3 presents the variation of daily affected area for the 1998/99 regional extreme drought event throughout the event's duration. Clearly, the results of the two indices were consistent from 17 December 1998 to 10 April 1999, but inconsistent—with large differences—at the beginning and ending stages of the drought event. CI's daily affected area appeared suddenly more than 200 km² at the beginning stage (11 November 1998); and then, during the ending period, IWAP's daily affected area dropped suddenly on 11 April 1999, whilst CI's daily affected area decreased gradually. Analysis of other extreme drought events listed in Table 2 (figures omitted) indicated that CI's unreasonable phenomena, as shown in Figs. 2 and 3, were commonplace rather than specific to this particular case.

By taking into consideration the variation of daily preci-pitation (Fig. 2) and the calculations (Eqs. (1)–(5)) for the two indices, the two unreasonable phenomena in CI's results could be understood as follows.

(1) On 23 November 1998, which was 30 days after the last rainfall on 24 October, Taiyuan suddenly entered a severe drought state from a normal state and, correspondingly, drought conditions suddenly appeared across a large area. The reasons for this were that the precipitation over the last 30 days (P₃₀) suddenly became 0, the relative moisture index over the last 30 days (M₃₀) was equal to –1.0, and the SPI over the last 30 days (Z₃₀) suddenly turned into an abnormally small value, in Eqs. (1) and (2).

(2) Later, mainly affected by the SPI over the last 90 days (Z₉₀), drought in Taiyuan area gradually alleviated up until 21 January 1999 (90 days after 24 October), even though there was no more precipitation during that period.

Based on the above analysis, the weights in Eq. (1) should be estimated again more carefully, with the weight of Z₃₀ made larger and the weight of Z₉₀ smaller. In addition, to understand the reason for the sudden decrease in the IWAP daily affected area,Fig. 4 displays the distribution of precipitation on 11 April 1999. It is seen that more than 10 mm of precipitation, which helped mitigate the drought, fell in most regions south of the middle and lower reaches of the Yellow River. The differences in the variation around 11 April 1999 between the results of the two indices indicated that IWAP was highly sensitive to the precipitation, whereas CI's reaction was notably lagged.

3.2 Comparison of general characteristics of drought events

In this study, the frequency of drought events was counted according to the start date of a drought event. For the CRMDEs, the total numbers were 174 and 184 during 1961–2010 based on CI and IWAP, respectively. The variations of the two frequencies both showed weak increasing trends, but with the CI trend being nearly twice that of the IWAP trend (Fig. 5), and the correlation coefficient between them was 0.49. In addition, rela-tively clear interdecadal variations existed in both of the two frequencies during 1961–2010.

Focusing on extreme and severe CRMDEs, the variations of the two frequencies both showed weak decrea-sing trends (Fig. 6), and the correlation coefficient between them was 0.6. Both of the two correlation coefficients (0.49 and 0.6) were statistically significant at the 0.01 level. In addition, clear interdecadal variations with peaks in both the 1960s and 1990s existed in both of the two frequencies.

Meanwhile, for extreme and severe CRMDEs, the variations of the two mean-integrated indices based on CI and IWAP both showed increasing trends, but with the CI trend being more than triple that of the IWAP trend during 1961–2010, and obvious interdecadal variations with peaks in both cases in the late 1990s (Fig. 7).

In addition, all the above increasing or decreasing trends were not statistically significant. Considering the two studies by An et al. (2014) and Li et al. (2014), this increasing trend in the mean-integrated index for extreme and severe CRMDEs shows good relationships with the increasing trends in both frequency and inten-sity of regional meteorological drought events in South-west and North China.

Figure 8 illustrates the seasonal variations of the monthly frequencies of extreme and severe CRMDEs based on CI (Fig. 8a) and IWAP (Fig. 8b), and the China-mean monthly precipitation (Fig. 8c), for 1961–2010. Investigation revealed that the correlation coefficient between the monthly frequency of extreme and severe CRMDEs based on CI and the China-mean monthly precipitation was –0.3, which was significant at the 0.05 level; whereas, that between the monthly frequency of extreme and severe CRMDEs based on IWAP and the China-mean monthly precipitation was –0.76, which was significant at the 0.001 level. How can we understand this result? Ding (2008) pointed out that, among the five drought-prone regions in China—Northeast, eastern Northwest and North China, the Yangtze River valley, South China, and Southwest China—the Yangtze River valley is the only one in which drought events frequently occur in summer; drought events in the other four regions frequently occur in autumn, winter, and spring. From Figs. 8a and 8b, even though both of the seasonal variations showed similar peaks in February and October, the result based on IWAP presented clearer seasonal features than those based on CI, i.e., the drought-prone period was from October to April and droughts rarely appeared during May and September, with no extreme and severe CRMDEs starting in June. These cha-racteristics coincide with the seasonal variations of the East Asian monsoon over central–eastern China, and are also consistent with the conclusion of Ding (2008) mentioned above, with the drought-prone period being exactly the dry season, and severe drought rarely occurring in the rainy season.

4 Summary and discussion

Based on the above analyses and discussions, a summary of the present study's findings can be drawn as follows.

(1) Compared with records of extreme drought events in studies such as Ding (2008),Zhang et al. (2009), and NCC (2002), the two drought indices CI and IWAP showed strong ability in identifying CRMDEs. The re-sults based on CI and IWAP were generally consistent, especially for high intensity (such as extreme and severe level) CRMDEs. During 1961–2010, the numbers of extreme CRMDEs based on CI and IWAP were 17 and 18, respectively, and the 1998/99 North China drought ranked No. 1 in both sets of results. At the same time, although the two frequencies of extreme and severe CRMDEs based on CI and IWAP both showed weak decreasing trends, the two mean-integrated indices showed increasing trends.

(2) The results based on CI and IWAP were sometimes inconsistent with respect to the start and end time of a CRMDE. Generally, CI CRMDEs showed two unreasonable phenomena: (1) Under non-drought conditions, a severe drought stage could suddenly occur over a large area; and (2) then, during the following period, drought could alleviate gradually in cases of non-precipitation. These phenomena occurred because of the effects of the monthly relative moisture index (M₃₀), the monthly SPI (Z₃₀), and the seasonal SPI (Z₉₀) in CI's calculation formula. In addition, IWAP was sufficiently sensitive to precipitation, whereas CI's reaction to precipitation involved a clear lag.

(3) The frequencies of extreme and severe CRMDEs based on IWAP showed clear seasonal variations. The drought-prone period was from October to April, with a peak frequency of 11 in February; plus, droughts rarely appeared during May and September, with no extreme and severe CRMDEs starting in June. This characteristic coincides with the seasonal variation of the East Asian monsoon over central–eastern China. However, the frequencies based on CI presented much weaker seasonal variations, with the drought-prone period being from February to April.

Actually, each index has its merits and weaknesses. While CI shows the weaknesses mentioned above, IWAP also has its limitations in that the values of the parame-ters N,a, and especially c in Eqs. (3)–(5) are relatively empirical, with the value of the parameter c limiting the application of IWAP in regions with annual average precipitation greater than 300 mm.

The above analyses and discussions show that, even though results based on CI and IWAP are generally consistent, obvious differences exist, and the reasons for those differences lie mainly in the formulae of the indices. There are implications, therefore, for the way in which we construct a meteorological drought index. Firstly, precipitation is the most important factor for a meteorological drought index, and the concept of a “precipitation anomaly” should be included in it, as drought essentially means a precipitation deficit. Even though other factors such as temperature or evapotranspiration can also have influences on the status of drought, it needs to be kept in mind that they are minor. Secondly, a good drought index for drought monitoring should absorb not only daily precipitation, but also the new concept of “effective precipitation” (Byun and Wilhite, 1999), as for the current drought/flood state the contribution of daily precipitation of a certain day before the current day will reduce as time passes. In this regard, the SPI is not a good method, as it does not absorb the daily-weighted-average concept, even though it can perform well in monthly or longer timescale drought assessments (Pashiardis and Michaelides, 2008). Thirdly, a good drought index should be dimensionless, so as to be suitable for broad application in different regions and seasons. In short, based on the above analyses, the IWAP drought index, which encompasses the three characteristics discussed above, possesses clear advantages in detecting and monitoring regional drought events. We conclude that the near-future prospects for IWAP in terms of its contribution to studying and monitoring drought are good.

Acknowledgments . The authors would like to express their deep appreciation to the three anonymous reviewers for their substantial contribution towards improving the quality of this article.