Drought Assessment by a Short-/Long-Term Composited Drought Index in the Upper Huaihe River Basin, China

Accurate and reliable drought monitoring is of primary importance for drought mitigation and reduction of social-ecological vulnerability. The aim of the paper was to propose a multiscale composited drought index (CDI) which could be widely used for drought monitoring and early warning in China. In the study, the upper Huaihe River basin above the Xixian gauge station, which has been hit by severe droughts frequently in recent decades, was selected as the case study site. The newly built shortterm/long-term CDI comprehensively considered three natural forms of drought (meteorological, hydrological, and agricultural) by selection of different variables that are related to each drought type. The short-term/long-term CDI was developed using the Principle Component Analysis of related drought components. The thresholds of the short-term/long-term CDI were determined according to frequency statistics of different drought indices. Finally, the feasibility of the two CDI was investigated against the self-calibrating Palmer drought severity index, the standardized precipitation evapotranspiration index, and the historical drought records.The results revealed that the short-term/long-termCDI could capture the onset, severity, and persistence of drought events very well with the former being better at identifying the dynamic evolution of drought condition and the latter better at judging the changing trend of drought over a long time period.


Introduction
Drought is one of the most damaging natural hazards and often results in devastating effects to social and ecological systems (Hao and Aghakouchak, [1]).The annual economic damage of severe droughts across China is estimated to be 2.5-3.5 percent of the gross domestic product.The frequency of severe and extreme droughts in China increased significantly from 26.8 percent during 1950-1990 to 47.6 percent during 1991-2011 [2], and the drought percentage area increased by 3.92 percent/10a from 1990s (Yu et al., [3]).Thus, accurate and reliable drought monitoring and prediction are of critical importance for risk assessment and decision making.Different drought indices have been developed and applied for drought monitoring and assessment.
The Palmer drought severity index (PDSI; Palmer [4]) and self-calibrating PDSI (scPDSI; Wells et al. [5]) are widely used for drought characterization.The standardized precipitation index (SPI; McKee et al. [6]) and the standardized precipitation evapotranspiration index (SPEI; Vicente-Serrano et al., [7]) are commonly used for meteorological drought monitoring.The standardization concept was also applied to other drought indices such as the standardized soil moisture index (SMI) and the standardized streamflow index (SSI, Vicente-Serrano et al., [8]).However, the performance of different drought index differs in detecting the drought onset, persistence, and termination.Wilhite [9] concluded that using a single index to reveal the diversity and complexity of drought conditions and impact is one of the major limitations to drought monitoring.Due to the fact that no single index 2 Advances in Meteorology can represent all aspects of meteorological, agricultural, and hydrological droughts, a multi-index approach should be proposed for drought monitoring, assessment, and prediction (Hao and Aghakouchak, [1]).Located in a transition zone between the climates of North and South China, the Huaihe River basin was determined to be the region being easily hit by floods and droughts frequently.Xie et al. [10] investigated the feasibility of six drought indices (Rainfall Anomaly Index (RAI), Z index, SPI index, Relative Moisture Index, Composited Meteorological Index (CMI), and modified CMI) in the Huaihe River basin during 1961-2010 and concluded that the CMI and the modified CMI were better at identifying drought events.Zhang et al. [11] assessed the drought condition of the upper Huaihe River basin by the PDSI and the RAI, and the result revealed that the RAI was much more sensitive than the PDSI in drought monitoring.Zhang et al. [12] analyzed the evolution of hydrological drought features under the regulation of two cascade reservoirs in the Huaihe River of China and indicated that although the downstream reservoir leads to an overall increase in the drought severity, it mitigates the severe and extreme droughts; the reservoir storage functions to smooth streamflow variation in that it reduces the drought frequency and extends the duration.Admittedly, the drought assessment and monitoring in the Huaihe River basin have been a focus of many meteorologists and hydrologists (Zhang et al., [13]; Cai et al., [14]; Wang et al., [15]; Duan et al., [16]; Yan et al., [17]).However, previous research on drought in the study area is mostly based on one single drought index or only considered one type of drought.The aim of this paper is to introduce and evaluate a shortterm/long-term composited drought index (S CDI/L CDI) which comprehensively considered three natural forms of drought (meteorological, hydrological, and agricultural) by selection of different variables that are related to each drought type in the upper Huaihe River basin.The output of the study could provide valuable references for the drought monitoring and early warning system development in the Huaihe River basin and other regions/basins in China.

Selection of CDI Components.
Based on the differences in time scales and drought types of drought index, the scPDSI, the 1-and 3-month SPEI, ZIND, and the SMI were selected to develop the short-term CDI by using the Principle Component Analysis (PCA), while the Palmer Hydrology Drought Index (PHDI), the 6-, 12-, 18-, and 24-month SPEI, the SSI, and the SMI were chosen to formulate the long-term CDI.The dynamic evolution of drought condition can be obtained by the short-term CDI while the changing trend of drought over a long time period could be known by the longterm CDI.

Principle Component Analysis.
The PCA method is a technique applied to multivariate analysis for dimensionality reduction [18].The original intercorrelated variables could be reduced to a small number of new linearly uncorrelated ones that explain most of the total variance.
Considering  variables in a given time period ,  ,1 ,  ,2 , . . .,  , ,  principle components (PCs) are produced for the same time period,  ,1 ,  ,2 , . . .,  , , using linear combinations of the first ones, according to In the applications the variables  , refer to scPDSI, SPEI1, SPEI3, ZIND, SMI, and series for short-term CDI, and refer to PHDI, SPEI6, SPEI12, SPEI18, SPEI24, SSI, and SMI series for long-term CDI. is equal to the number of drought indices (5 for short-term CDI and 7 for long-term CDI) and  represents the length of drought indices series.
In (1)  ,1 explains most of the variance,  ,2 explains the reminiscent amount of variance, and so on.PCs extraction could be based on variance/covariance or correlation matrix of data with { 11 ,  21 , . . .,  1 } being the first eigenvector and { 11 ,  21 , . . .,  1 } being the eigenvector of  order and each eigenvector includes the coefficients of the  principal component.Finally, the amount of variance explained by the first PC is called the first eigenvalue  1 , and the second is  2 , so that  1 ≥  2 ≥ ⋅ ⋅ ⋅ ≥   .Since each eigenvalue represents the fraction of the total variance in the original data and is explained by each component, proportion of each component can be calculated as   / ∑   .Thus, the short-term/long-term CDI can be expressed as follows: where   is eigenvalue of the th principal component,  , is the th principal component of the th month, CDI  is the short-term/long-term CDI in the th month.

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And the long-term CDI can be formulated as follows: where   are eigenvalues of the th principal component,  , are eigenvectors of the th principal component of the th month,   is the drought index series in the th month, S CDI  and L CDI  are the short-term CDI and the long-term CDI in the th month.
It should be noted that the monthly scPDSI, ZIND, PHDI, and SPEI (in time scales of 1-month, 3-month, 6-month, 12month, 18-month, and 24-month, resp.) could be obtained based on the daily air temperature and precipitation from meteorological stations in/around the study basin, while the monthly SMI and the SSI need to be calculated by soil water volume and generated runoff based on the hydrological modelling.The gridded Xinanjiang model (XAJ; Zhao, [19]), a model of runoff formation on saturation of storage, used widely in humid and semi-humid regions in China, was adopted to simulate the gridded soil water and generated runoff in the upper Huaihe River basin.

XAJ Model.
The XAJ model is a rainfall-runoff, distributed, basin model for use in humid and semi-humid regions.The evapotranspiration component is represented by a model of three soil layers.Runoff production occurs on repletion of storage to capacity values which are assumed to be distributed throughout the basin.Prior to 1980, runoff was separated into surface and groundwater components using Horton's concept of infiltration.Subsequently, the concept of hillslope hydrology was introduced with an additional component, interflow, being identified.Runoff concentration to the outflow of each subbasin is represented by a unit hydrograph or by a lag and route technique.The damping or routing effects of the channel system connecting the subbasins are represented by Muskingum routing.There are fifteen parameters in all, of which the model is particularly sensitive to six.Optimization of the parameters is achieved with different objective functions according to the nature of each parameter.The model has been widely used in China since 1980, mainly for flood forecasting, though more recently it is also being used for other purposes.the short-term drought components with different drought intensity level in the upper Huaihe River basin above the Xixian station; secondly, average  , for the same drought intensity level, and then a series of new drought frequencies   ( for the drought intensity level) of different drought intensity levels for the short-term CDI was obtained; thirdly, determine the drought intensity threshold levels of the short-term CDI according to   .The drought intensity threshold levels of the long-term CDI can also be acquired by following the above steps.

Application of the Short-/Long-Term CDI
3.1.Case Study Site.The Huaihe River basin is one of seven major river basins in China and lies in the warm temperature semi-humid monsoon region, which is a transition zone between the climates of North and South China.Special geographical location determined that the Huaihe River basin was a region easily hit by floods and droughts over many centuries, particularly in recent decades, and severe droughts occurred much more frequently which caused huge economic and social loss.To propose a short-/long-term CDI which could be widely used for drought monitoring and early warning in China, this paper selected the upper Huaihe River basin above Xixian gauge station as the case study site with a catchment area of 10 190 km 2 (see Figure 1).

Data Preparation and Processing.
Considering the spatial unevenness of underlying conditions and meteorological variables, the study areas were divided into grids with a size of 1 km × 1 km.Based on the daily observed meteorological variables (precipitation and air temperature) from closer six meteorological stations during 1988-2005, the inverse distance-squared weighted method was used to acquire the meteorological data for every grid.Before the interpolation,  1 and 2).The result revealed that the daily XAJ model was simulated with satisfactory accuracy, which indicated that the calculated gridded soil water and generated runoff could be used for the further CDI construction.The monthly gridded SMI and SSI were computed based on the gridded soil water and generated runoff, and then the areal monthly SMI and SSI were carried out by averaging the gridded values.It should be noted that the soil field capacity was obtained from the International Geosphere-Biosphere Programme (IGBP) which provides the gridded Profile Available Water Capacity with the spatial resolution of 10 km × 10 km. Figure 2 showed the temporal variations of the areal averaged soil moisture index in the upper Huaihe River basin.

Application of the Short-/Long-Term CDI.
Based on the time series of areal monthly scPDSI, ZIND, 1-month SPEI, 3month SPEI, and SMI, according to (3), the short-term CDI in the upper Huaihe River basin above the Xixian station was carried out with the SPSS package.The eigenvalues and eigenvectors in (3) can be referred to in Table 3.And the drought intensity threshold levels of the short-term CDI were determined according to Section 2.5 (Table 4).
Based on the time series of areal monthly PHDI, 6-month SPEI, 12-month SPEI, 18-month SPEI, 24-month SPEI, SSI, and SMI, according to (4), the long-term CDI in the upper Huaihe River basin above the Xixian station was carried out   with the SPSS package.The eigenvalues and eigenvectors in (4) can be referred to in Table 3.And the drought intensity threshold levels of the long-term CDI were determined according to Section 2.5 (Table 4).values and the basin was in relatively dry condition in 1990s and early 2000s.Similar variation trends were also found in the L CDI and the PHDI and the L CDI and the 6-month SPEI time series (Figure 4).Correlations between the CDI and scPDSI/SPEI time series were also investigated by the Spearman correlation coefficient, which is the application of the Pearson correlation coefficient performed upon data ranks instead of the data themselves (e.g., Wilks., [20]), with the range of the Spearman coefficient being constrained within ±1.Rank correlation is a robust measure that is insensitive to the underlying data distribution and is recognized as a competent tool for determining the best aggregate correlation (Wilks,[20]).

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Rank correlation between the S CDI and scPDSI/1month SPEI was found to behave similarly to that between the L CDI and PHDI/6-month SPEI, that is, Spearman correlation coefficients being of 0.83, 0.72, respectively, between the S CDI and the scPDSI, and the S CDI and the 1-month SPEI time series, and Spearman correlation coefficients being of 0.75, 0.82, respectively, between the L CDI and the PHDI, and the L CDI and the 6-month SPEI time series.
The variation trends of all the drought indices are consistent with each other; however, the drought severity, onset, and termination identified by different drought indices varied differently.

Drought Assessment of Critical Drought Events.
Two critical drought events-the long-term 2000 drought and the short-term 1996 drought-were used to assess the fidelity of the S CDI, the L CDI, and their drought components.

Historical Records of Critical Droughts.
The 2000 drought, which actually began from September of 1999 and developed to the severe spring and early summer drought dry condition of the short-term drought event in 1996.It indicated that the S CDI could well capture the relative timely dynamic variation of the short-term drought evolution.

Drought in 2000.
Both the S CDI and the 1-month SPEI identified extreme droughts in March and April of 2000.However, the extreme drought continued developing till May of 2000 and it was only detected by the S CDI, while no drought was found by the 1-month SPEI (Figure 6(a)).In the meanwhile, severe drought was detected by the scPDSI.From Figure 6(b), the L CDI identified extreme droughts in March-May of 2000 while the 6-month SPEI identified this extreme drought only in April and May.Moreover, moderate drought was also detected from November of 1999 to January of 2000 by the L CDI, while almost no drought occurred identified by the 6-month SPEI.Severe drought was detected by the PHDI only in April and May.The above comparison demonstrated that the S CDI and L CDI best characterized the extreme drought in 2000.Since this drought persisted a relatively long time period, the L CDI was better identifying the whole drought evolution since the L CDI detected the severe drought in September of 1999 while the S CDI did not judge accurately.

Dynamic Spatial Distributions of Typical Drought Events.
Dynamic spatial distributions of the S CDI and its components in the upper Huaihe River basin were presented in Figure 7.A small part of the basin was firstly found in extreme drought in January 2000 by SMI with the rest in severe drought, while the 1-month SPEI identified the boundary area in extreme drought condition in March 2000 with the rest in severe drought condition.No extreme drought was found by the 3-month SPEI until April and May 2000.The S CDI discovered moderate drought in January and February 2000, and most part was discovered in extreme drought in March 2000, almost all basin in extreme drought in April and May 2000, and no drought in June 2000.The scPDSI and the ZIND only identified mild drought over the whole period.In general, the S CDI performed better than any other drought components; however, it was not the best choice while in comparison with the historical records of the 2000 drought.Figure 8 showed dynamic spatial distributions of the L CDI and its components in the upper Huaihe River basin.Almost the whole upper Huaihe River basin was in extreme drought condition in December 1999 by the L CDI, and such drought condition continued to May 2000, and the dry condition relieved in June 2000.The SPEI with different time scales only discovered severe drought during the period, and moderate drought was discovered by SSI and only mild drought by PHDI.Comparing Figures 7 and 8, it can be concluded that the L CDI best described the drought process, including the drought onset, severity, and termination month.

Conclusions
The short-term/long-term CDI were developed and applied in the upper Huaihe River basin.The performance of the short-term/long-term CDI was compared with their drought index components and historical records, respectively.The result revealed that the newly built short-term CDI could better capture the drought severity, onset, and termination than the scPDSI and the 1-month SPEI for relatively shortterm droughts, while the long-term CDI behaved better than the PHDI and the 6-month SPEI on drought persistence and magnitude for relatively long-term droughts; the S CDI is better at drought assessment of short-term drought events while the L CDI is better at drought assessment of long-term drought events; to obtain a more comprehensive and accurate result during drought assessment, the S CDI is suggested to be adopted for drought assessment during drought initial period while the L CDI is used after the drought persisting for a relatively long time period.The output of the paper could provide valuable references for drought estimation and monitoring of other river basins/regions in China.

Figure 1 :
Figure 1: Sketch map of the upper Huaihe River basin.

Figure 2 :
Figure 2: Temporal variations of the SMI in the upper Huaihe River basin.

Table 1 :
Calibrated parameters for the daily Xinanjiang model in upper Huaihe River above the Xixian station.
digital elevation model was used to correct the meteorological variables according to meteorological variable-elevation relationships.Monthly gridded scPDSI, ZIND, PHDI, and SPEI (1-month, 3-month, 6-month, 12-month, 18-month, and 24-month, resp.) was calculated on the basis of the gridded meteorological variables, and then the monthly areal drought indices were obtained by averaging their gridded values.3.3.Application of the XAJ Model.Based on the topography, hydrological, and meteorological data in 1988-2005, the daily gridded XAJ model was adopted to simulate gridded soil water and generated runoff in the upper Huaihe River basin above Xixian station.The calibration and validation periods were1988-2002 and 2003-2005, respectively (Tables

Table 2 :
Calibration and validation results of the daily XAJ model in the upper Huaihe River basin. is for precipitation,   for observed runoff,   for calculated runoff, and RE for relative error. Note:

Table 4 :
Drought categories of the short-term/long-term CDI.