A robust ensemble drought index: construction and assessment

Drought indices have been widely used in drought monitoring and assessments, but it is difficult to select a uniform index suitable for different geographical and climatic conditions. In addition, the statistical parameters of drought index also vary with fitting reference period, which brings more challenges to the practicality of drought index under climate change. In this study, a new multitimescale and more robust integrated drought index, the EDI was constructed by integrating the common components of seven single drought indices (including SPI, PDSI_th, PDSI_pm, scPDSI_th, scPDSI_pm, SPEI_th and SPEI_pm). The EDI was compared with the single drought index over China in terms of the occurrence ability of historical drought events, the dependence of statistical parameters on reference periods, the goodness-of-fit of standard normal distribution and the correlation with soil moisture and runoff. We find that the EDI could more accurately reproduce the location and intensity of historical drought events, reduce the uncertainty caused by both potential evapotranspiration estimation and the reference period, has higher goodness-of-fit of standard normal distribution, higher correlation with soil moisture, more robust performance in hydrologic drought monitoring and less affected by the difference of geographical and climatic conditions. Moreover, the EDI improved the accuracy of drought monitoring in arid and semiarid regions of China, where assessment is always complex. Furthermore, the available evidence supports that a long-term stationary climate variables series could provide more accurate drought assessment.


Introduction
Drought is a periodic extreme climate phenomenon that is usually triggered by below-normal precipitation (Ding et al. 2021), leading to the shortage of available water resources for some activities or some groups (Heim 2002;Mishra and Singh 2010). As a result of the temporal variability of climate factors, drought may occur in most regions of the world, rather than only in arid areas, and drought provokes considerable damage to agriculture, natural resources and society (Li et al. 2015;Zhang and Zhou 2015;Byakatonda et al. 2018;Song et al. 2020;Zhang et al. 2020;Mokhtar et al. 2021;Rahmani and Fattahi 2021;Puangbut et al. 2022). Scientifically copping with this phenomenon, the strong drought indices should be used first to obtain monitoring data .
In consequence of the slow development and long duration of drought, it is difficult to build a physical quantity that can accurately quantify the effect of drought in various systems. In addition, the response of a water resource system to drought is complex, and the properties of the system will in turn affect drought (Mishra and Singh 2010;Zhang et al. 2020). In recent decades, drought indices have become an effective tool used to monitor and quantify drought (Vicente-Serrano et al. 2013;Yang et al. 2017). These indices provide reasonable assessments of the severity, intensity, starting time and ending time of drought and are comparable in time and space. However, the application of drought indices is limited by less recorded historical data (such as soil moisture and river runoff), which indicates that complex indices may perform poorly due to unreal observation records (Mokhtar et al. 2021). Therefore, meteorological drought indices, especially the PDSI (Palmer 1965), scPDSI (Wells et al. 2004), SPI (McKee et al. 1993) and SPEI (Vicente-Serrano et al. 2010), have been widely used by using climate variables with reliable historical records as input Shilenje et al. 2019;Tigkas et al. 2019;Zarei et al. 2021;Mokhtar et al. 2021;Ghasemi et al. 2022;Pandžić et al. 2022;. The use of soil data and total water balance methods allows it to determine drought very conclusively, the PDSI has been reasonably successful at quantifying long-term drought, such as agricultural and hydrological droughts (Dai et al. 2004;Dai 2011b;Sheffield et al. 2012). In addition, the introduction of temperature data allows PDSI to capture the basic effects of global warming on drought through changes in potential evapotranspiration. But, the PDSI cannot describe the multitimescale characteristics of drought systems or ensure consistency in space (Zhuang et al. 2013;Beguería et al. 2014;Liu and Jiang 2015) and also has the problem that the assumptions of a physical model are unrealistic and empirical (Mishra and Singh 2010). The scPDSI was developed to correct the spatial inconsistency of the PDSI, leaving other problems of the PDSI unsolved (Wells et al. 2004). Considering the multitimescale characteristics of drought systems and taking advantage of statistics, the SPI was designed (McKee et al. 1993). The SPI has undergone rigorous statistical testing (Guttman 1998) and has been shown to be effective in detecting the early emergence of drought. Precipitation is the only input parameter, so the SPI is less complex than many other indices. However, the SPI can only quantify the precipitation deficit, which limits its usage in some arid and semiarid areas. Moreover, values based on preliminary data may change, and values change as the period of record grows, so it is not suitable for the analysis under climate change. The SPEI considers both precipitation and potential evapotranspiration on the basis of the SPI. The inclusion of temperature and precipitation data allows SPEI to consider the influence of temperature on drought development through basic water balance calculations, so it can be used to examine climate change impacts under different future scenarios (Vicente-Serrano et al. 2010). Neither the SPI nor the SPEI fully accounts for the role of the underlying surface in the drought assessment. Moreover, it is difficult to ensure the reality of a prior hypothesis distribution for fitting, especially in arid and semiarid regions (Mishra and Singh 2010). The difference of applicable conditions of drought index makes it difficult to compare drought among regions.
Furthermore, due to the global warming, both the frequency and the intensity of extreme climate events have increased significantly (Zarch et al. 2015). In most parts of China, with a significant increase in temperature , precipitation shows more uncertainty and more short-term local heavy rainfall events (Pei et al. 2022). The stochastic and nonlinear changes in meteorological elements under a climate change background lead to variability in statistical characteristics of existing drought indices, which challenges the applicability of statistical methods and makes accurate drought assessment more difficult. Existing studies have shown further desiccation with an increasing trend in the frequency and intensity of drought events, and the situation may become more serious in the future Xu et al. 2021). Therefore, it is essential to develop a robust drought index with less dependence on climate change for practical application. However, the complexity of drought and the diversity of drought systems hinder the development of a single drought index that can be fully applied to drought monitoring in all regions and under all climatic conditions (Heim 2002;Mishra and Singh 2010;Wang et al. 2017).
Although the PDSI, the scPDSI, the SPI and the SPEI have their own advantages and limitations and focus on different physical and biological processes, their strengths can partly compensate for each other's weaknesses to some degree, and thus, they are likely to contain consistent components that would allow for more objective and reliable conclusions by extracting the common components of each of these indices (Guttman 1998;Heim 2002;Li et al. 2015;Chen et al. 2017).
Here, aiming at more robust drought event assessment and a wider range of applicability in different drought systems, we constructed a multitimescale integrated drought index, the ensemble drought index (EDI), by integrating the SPI, PDSI, scPDSI and SPEI. The timescales of the SPI and SPEI used in this study were 3, 6, 9 and 12 months; hence, the EDI was the same. These timescales were consistent with the applicable scenarios of the PDSI (Dai et al. 2004;Dai 2011b). Recognizing that both the potential evapotranspiration calculation method and the reference (calibration) period for fitting parameters will lead to a certain impact on the accuracy of the indices, we first selected the Thornthwaite method (Thornthwaite 1948) and the Penman-Monteith method (Allen et al. 1998) to calculate two sets of indices as described in Sect. 2.2 for the construction of the EDI. Second, we selected three different reference periods with differences in the trend of observation records as described in Sect. 2.3 for comparison of the time series and statistical characteristics, as well as the test of applicability in different aspects among indices involved in this study in Sects. 3 and 4. The results of the comparisons mentioned above indicate that the EDI will enable drought to be monitored more efficiently.

Data and data preprocessing
The observation data used in this study were from the Meteorological Data Network of China (http:// cdc. cma. gov. cn/). Daily routine surface observation data of China covered the period of 1960-2019, including precipitation, temperature (maximum, minimum and average temperature), surface air pressure, wind speed, relative humidity and sunshine duration. This dataset was repeatedly tested and controlled before release. A total of 635 stations with less than 1% missing records were selected (Fig. 1), the average percentage of data missing of 635 stations are 0.15%, 0.07%, 0.08%, 0.10%, 0.14% and 0.12% for precipitation, temperature, surface air pressure, wind speed, relative humidity and sunshine duration, respectively. The soil water capacity dataset was from Dai et al. (2013). The soil water content data were part of the GLDAS-2.0 dataset. The coastal runoff of the Yangtze River and the Yellow River was from the dataset published by Dai (2016), which covered only the period of 1948-2000. For the missing data, we adopted the following interpolation method to ensure the continuity of data. We used the following interpolation methods to restore the missing temperature data: (1) For the data missing for no more than 5 consecutive days, linear interpolation was used based on the two nearest valid temperature values to the two end dates of the missing data period; (2) For the data missing for more than 5 consecutive days, one linear regression equation was used to restore the missing data, in which the year as the independent variable and the valid temperature value as the dependent variable. Due to the complex influencing factors and nonlinear variation of precipitation, it is difficult to interpolate precipitation data, the missing precipitation data was simply replaced by 0. The others were replaced by their respective average valid data at the same date in each year. Net radiation was estimated using the FAO Penman correction formula recommended by Gao et al. (2013).

Estimation of potential evapotranspiration
PET is one of the main inputs for drought indices, and ET 0 is generally used as the estimate of PET. One of the widely used methods is the Thornthwaite method, which uses only temperature and latitude as inputs. However, global warming and wind speed weakening make the estimation of ET 0_ th deviate from reality (Dai 2011b;Sheffield et al. 2012;Liu and Jiang 2015;Zhang et al. 2016); then, we used the modified Thornthwaite formula (Willmott et al. 1985) to further limit the effect of temperature. The FAO Penman-Monteith method recommended by the FAO (Allen et al. 1998) for ET 0 estimation (ET 0_ pm) has a more reliable theoretical basis and has proven feasible in both dry and humid regions (Seneviratne 2012). However, the Penman-Monteith method requires many complex variables as inputs, which are sparsely observed or rarely recorded, and most of them suffer changes in the main observation methods (Sheffield et al. 2012), so it is difficult to guarantee the authenticity of the inputs. Whether ET 0 estimation methods significantly affect drought indices has been a contentious topic among many studies (Dai 2011a;Sheffield et al. 2012;van der Schrier et al. 2013;Zhang et al. 2016;Chatterjee et al. 2021), and it is difficult to draw accurate and reliable conclusions (Dai 2011a;Sheffield et al. 2012;van der Schrier et al. 2013;Zhang et al. 2016;Chatterjee et al. 2021). To eliminate the influence of the ET 0 calculation method on the results as much as possible, we calculated the PDSI, scPDSI and SPEI indices using the modified Thornthwaite and the FAO Penman-Monteith methods for comprehensive analysis, respectively.

Reference period
Statistical drought indices (such as the PDSI, scPDSI, SPI and SPEI) involve calibration (standardization) in time and space, which means that they are affected by the reference period for fitting statistical parameters (Sheffield et al. 2012;Um et al. 2017). This indicates that the trend of climate variables in the reference period will lead to differences in the same index, and the significant difference appears only outside the reference period, which may lead to misleading results (Sheffield et al. 2012;Um et al. 2017). In climate 1 3 research, it is customary to describe climate characteristics in 30-year periods (Zhang and Zhao 2022). In most cases, the 30-year climate element series usually is not stationary sequence, but a relatively stable factor value can still be obtained, so the reference period should not be less than 30 years. To understand how different reference periods affect drought indices under global warming, we selected three different reference periods (Table 1): (1) there was no significant trend in temperature and PET during REF1; (2) there was a significant trend in temperature and PET during REF2; and (3) REF3 was the record duration of the surface observation data.

Principal component analysis
PCA transforms a group of possibly correlated variables into a group of linearly uncorrelated variables (called principal components) by orthogonal transformation, and the amount of information of each principal component is usually measured by variance. Mathematically, the processing of the principal component is equivalent to a linear combination of input drought indices to form a new comprehensive index. We hope to derive PC1 from the original drought indices so that they can retain as much consistent information as possible in the original variables and reflect the drought situation more accurately.
All data processing, element estimation and drought index calculations were performed using Python in this study.

Temporal variation in drought in China in the past 60 years
When the timescale was determined, the same reference period led to a similar trend (Figs. 3, 4, 5, 6) and a significant positive correlation between each index (p < 0.01) among the SPI, PDSI_th, PDSI_pm, scPDSI_th, scPDSI_pm, SPEI_th and SPEI_pm, many studies have confirmed the positive correlation among drought indices (Yang et al. 2017;Wable et al. 2019). Moreover, the correlation increased with increasing timescale, which also indicated the feasibility of PCA. The minimum correlation coefficient appeared between scPDSI_th and SPEI_pm (REF1: 0.38-0.58; REF2: 0.38-0.53; REF3: 0.46-0.59) in all cases. Generally, the duration of the drought period was longer than that of the humid period in the past 60 years, while the frequency of extreme events presented the opposite trend. The development of dry and wet conditions was mainly affected by precipitation. However, since 1980, the effect of ET 0 on the dry and wet conditions gradually increased (Fig. 2). During this period, the intensity and duration of drought showed an obvious upward trend, which is basically consistent with the existing research results (Chen and Sun 2015;Wang et al. 2017). After 2011, severe drought began to ease gradually, and then  1960-19971960REF2 19801960REF3 19601960 a humid period began, which was mainly affected by the significant increasing trend in precipitation (Fig. 2a).
In the past 60 years, the average ET 0 _th had a significant upward trend (p < 0.05), while ET 0 _pm had no significant trend, which made the modified Thornthwaite method more likely to overestimate drought events and underestimate humid events than the FAO Penman-Monteith method (Figs. 3, 4, 5, 6). Different reference periods also led to differences in drought indices (Figs. 3, 4, 5, 6). When using ET 0 _th, calibration based on REF1 led to a smaller value of drought indices (more prone to drought), while REF2 led to a larger value (Fig. 7). Considering the FAO Penman-Monteith method, there was no significant difference between indices based on REF1 and REF2, which was because ET 0 _pm showed no significant trend in both reference periods. However, using REF2 led to different results between PDSI_pm/scPDSI_ pm and SPEI_pm. This may be because the variable used in the calculation of the PDSI and scPDSI is the actual evapotranspiration (ET), which is estimated via ET 0 (Dai 2011b), rather   (Fig. 7). This indicates that the trend in climate variables and ET 0 estimation method will affect the accuracy of drought indices, though the effect could be eliminated by a longer reference period, which is consistent with the research of Sheffield et al. (2012).   Guttman (1998) recommended discarding the previous four years in the PDSI series to ensure the reliability of the analysis results. Therefore, the period covering 1964-2019 was selected for all indices analyzed above. To ensure that the original statistical significance of drought indices did not change, numerical domain scaling was used (i.e., using PDSI/2 and scPDSI/2 for PCA) instead of standardization so that each index after preprocessing had the same drought grade classification. This means that the value of the eigenvector at each  We used 24 different sets of index series for PCA: (1) three types of reference periods, (2) 3-, 6-, 9-and 12-month timescales, and (3) using the entire series and series during 2000-2010. In 24 cases, the North test showed that the first principal component (PC1) of each station had reached a significant level. Moreover, the variance contribution rate of the first principal component was more than 60%, and most regions were more than 70% in all cases, which increased with increasing timescale. The region with the largest variance contribution rate was mainly concentrated in southeastern China, and the region with the smallest rate was around the junction of XJ, QH and GS provinces, which may be related to the applicability of the selected drought index in dry and semidry areas.

Ensemble drought index and its temporal variation
In all cases, the eigenvector of PC1, denoted as u = u 1 , u 2 , … , u 7 , satisfies Eq. (1): In Eq. (2), u i is the ith component of the eigenvector.
The following inequality can be obtained: In Eq. (3), the grade classification of PC1 is not consistent with that of SPI/SPEI. To solve this problem, the vector v = v 1 , v 2 , … , v 7 is defined by Eq. (4): which satisfies Eq. (5): The values of seven single drought indices, described in Sect. 3.1, are recorded as a column vector denoted as x at each station at timescale t: In Eq. (6), x T is the matrix x transpose. The ensemble drought index (EDI) at timescale t is defined as follows: In Eq. (7), w = v 1 , 0.5v 2 , 0.5v 3 , 0.5v 4 , 0.5v 5 , v 6 , v 7 , and x is the mean column vector composed of the multiyear average values of the indices of the station.
Based on the PCA results of the above 24 cases, we found that the eigenvectors of PC1 had similar results in all cases except for some stations in Northwest China and other scattered regions. After eliminating the abnormal sites, the average value of eigenvector w of each case and station was obtained as the empirical estimation (denoted as w * ) of w over China, w * can be represented by Eq. (8): Figure 8 shows that the EDI detected the main drought periods of 1970-1972, 1978-1983, 1986-1988 and 1999-2010 and retained the characteristics of multitimescale indices. It also showed that although there was a long drought period in China during 1999-2000, the intensity of drought slightly increased only in a few years compared with those indices calculated with ET 0 _th, which indicated that the EDI eliminated the influence between the modified Thornthwaite and FAO Penman-Monteith methods. Moreover, the influence of the reference period on the EDI was weakened. In contrast to the EDI, some single drought indices depend seriously on ET 0 (e.g., PDSI, Palmer 1965) and the length of data series (e.g., SPI, Guttman 1998;Wu et al. 2005;Vicente-Serrano et al. 2010), so the EDI could make the evaluation results more comparable in time and space. As the reference period had little influence on the EDI, only the REF1 reference period is plotted in Fig. 8.

The reappearance ability of the EDI in historical drought events
The ability to reproduce historical drought events in China is an important criterion to evaluate the applicability of drought indices. Referring to relevant studies (Wang and Chen 2014;Zhang and Zhou 2015;Wang et al. 2017), 6 typical large-scale severe drought events in China were selected, as shown in Table 2, to verify the EDI. We found that the spatial distributions of the PDSI_pm, scPDSI_pm, SPI, SPEI_pm, and EDI in those typical drought years were relatively similar, except for the location and range of the dry and wet centers (Fig. 9). All these reappearances were consistent with the description in Table 2. The atlas "Yearly charts of dryness/wetness in China for the last 500-year period" edited by the Chinese Academy of Meteorological Sciences (CAMS 1981) and its two interpolations   (Zhang and Liu 1993;Zhang et al. 2003) are widely used in scientific research and practical business. We considered them as a reference of reality and found that the EDI could most accurately describe the main region, location and intensity of both dry and wet disaster centers among the indices mentioned above. In addition, we found that the reference period led to obvious differences in the spatial distribution of the EDI in 2000 and 2009 (Fig. 10). By comparison with the disaster records, the EDI calibrated by REF1 could more accurately reflect the regional drought situation.

Tests of goodness-of-fit to the EDI
According to the definition of drought, the distribution of the drought index is expected to follow the standard normal distribution, which indicates that the goodness-of-fit test is a method that can be used to determine the applicability of the drought index (Stagge et al. 2015;Vicente-Serrano and Beguería 2016). The Kolmogorov-Smirnov (K-S) nonparametric test was used in the goodness-of-fit test. The data series for the test were from January to December at each station, and 0.05 was selected as the critical threshold to reject the original hypothesis. When the p value is greater than 0.05, the index series follows the standard normal distribution. However, the p value cannot be used to evaluate the goodness-of-fit, and the failure rate of all stations should be used (Vicente-Serrano and Beguería 2016). As the SPEI_pm had the lowest failure rate among the indices participating in PCA, it was set as a control group. The results (

Fig. 9
Spatial distribution of a the PDSI, b the scPDSI, c the SPI, d the SPEI_pm and e the EDI on the 3-month timescale based on REF1 in five major drought years eliminate the tendency to deviate from the normal state caused by the reference period, which means that the index series of more stations followed the standard normal distribution. Considering indices based on REF3, the EDI may be able to retain the true tendency toward dry or wet in some regions.

Applicability evaluation of agricultural drought
The easiest way to test the applicability of the EDI in agricultural drought monitoring was correlation analysis between the newly constructed index and the benchmark index (such as  the PDSI and SPI). However, the PCA algorithm makes this method invalid, which means that soil moisture (considered a proxy of agricultural drought development) must be used for this purpose (Dai et al. 2004;Dai 2011b;Yang et al. 2017). The correlation analysis was processed between the soil moisture and the PDSI, scP-DSI, SPI, SPEI and EDI in the warm season (April to October) during 1964-2014 in the GLDAS-2.0 dataset. The results showed that all the above indices had a positive correlation relationship with soil moisture (p < 0.01), with the positive correlation relationship between the SPEI_pm and soil moisture being the most significant. Therefore, the SPEI_ pm3/6 and EDI3/6 were selected for the following comparison. Due to the difference in the reference period leading to little discrepancy, both figures were based on REF3 (Fig. 11). The applicability of the EDI was similar to that of SPEI_pm in most of the humid areas of Southeast China and was slightly worse than that of the SPEI_pm in the humid areas of the middle and lower reaches of the Yangtze River and Eastern LN. We found that the EDI had better performance than the SPEI_pm in the dry, semidry and most semi-humid areas of North China, as well as in some regions of Southwest China, which means that the EDI can overcome the common disadvantage of drought indices.

Applicability evaluation of hydrologic drought
Similar to Sect. 4.3, river runoff must be used for this evaluation. The average monthly runoff of the Yangtze River and Yellow River estuary stations in Dai's dataset was selected. Due to the complexity of topography and geomorphology, the confluence process of precipitation may have an impact on river runoff after several weeks or months, so the correlation analysis used the yearly data of the runoff and drought index (Dai 2011a). Figure 12 shows the annual series of the average values of drought indices and their coastal runoff in the Yellow River and Yangtze River basins from 1961 to 2000. For the Yellow River basin, the PDSI_pm had the best correlation, while for the Yangtze River basin, SPI12 was the best. This means that the applicability of the drought index was different with the variation in regions, and it was difficult to select the most suitable hydrological drought index for each climate region. The correlation coefficient of EDI12 and runoff in the two cases ranked at the top of the list among all indices, indicating that the EDI had good applicability regardless of geographical and climatic differences (Fig. 12). In addition, the ability of the EDI to monitor hydrological drought was closely related to the timescale, and the most appropriate timescale was different with respect to regions, especially in northern China, where the spatial change in the appropriate timescale was very large (Wang and Chen 2014). The 12-month timescale selected here may limit the ability of the EDI to monitor hydrological drought. Because the results of the correlation analysis between the PDSI and scPDSI were similar, only the PDSI was given here. REF3 was selected as the reference period for calibration. Similar results were obtained based on REF1 and REF2.

Conclusion
We constructed a new integrated drought index, the EDI, for more efficient drought monitoring and reveal some traps for drought assessment in the context of climate change. In this study, the SPI, PDSI_th, PDSI_pm, scPDSI_th, scPDSI_pm, SPEI_th and SPEI_pm were selected, and calculations were based on three different reference periods. The EDI was more robust in both time and space than other single drought indices under various 1 3 drought systems and could be used in regions without an in-depth study of drought or in those with a lack of feasible drought monitoring indices.
The PCA method was used to extract the common components of those selected drought indices. In terms of the first principal component (PC1), the variance contribution rate in the study area reached a relatively high level. Considering the trade-off between the statistically significant level and application simplicity, the EDI was constructed by mapping with a transformed eigenvector of PC1. We also adopted an empirically transformed eigenvector Fig. 11 The distribution of a r EDI3 minus r SPEI_pm3 , b r EDI6 minus r SPEI_pm6 shows the differences in applicability that was suitable for drought monitoring in the study area, as did the EDI calculation formula. We evaluated the advantages of the EDI and found that the EDI could correct the deviation from the expected normal distribution, retain the properties of multitimescale indices for flexible usage and weaken the influence of the reference period and ET 0 estimation method. The EDI could more accurately reproduce the disaster region, center location and intensity of both the major drought and the wet events in history and could perform well in both agricultural and hydrological drought monitoring in comparison with other single drought indices. The EDI showed some good properties and stable applicability regardless of climatic region, geographical condition or drought system, especially in the Fig. 12 a Location of stations in the Yellow River basin and Yangtze River basin. The annual mean 12-month EDI, SPI, PDSI_pm, PDSI_th, SPEI_pm and SPEI_th in the b Yellow River basin and c Yangtze River basin arid and semiarid regions in North and Southwest China where drought monitoring faces great difficulties (Mishra and Singh 2010;Pei et al. 2022).
Comparison among those indices showed that both the potential evapotranspiration estimation and the reference period led to variability in the statistical characteristics of the drought indices, which was mainly caused by non-stationary observation data series. Furthermore, this kind of influence could be more complicated, involving the differences in the physical models of drought indices, as well as other variable estimations. These difficulties indicated that drought indices require careful and wide examination before practical usage. For the purpose of more reliable drought assessment and analysis, the period with the long record and no significant trend in climate variables should be selected as the reference period for calibration.
The EDI also faces some limitations. The foundation of the EDI was the significant pairwise correlation of drought indices involved in PCA. However, in most areas, the PDSI/scPDSI has a significant correlation only with the SPI/SPEI at medium-and longterm timescales (Vicente-Serrano et al. 2010), which means that for shorter timescales (such as 1 month, 2 months or shorter), there may be problems in the effectiveness of the integrated drought index constructed by a linear transformation of PC1. In regions that are more sensitive to short-term water deficits, a drought index with a shorter timescale may be more suitable for agricultural drought and forest fire risk monitoring (Heim 2002;Vicente-Serrano et al. 2013), which indicates that the EDI has limited applicability in these areas, and the optimal timescale for different drought systems needs further research. Therefore, in those regions, it is necessary to select a variety of meteorological drought indices that can reflect the changes in short-term water deficits for reasonable integration.