Drought structure based on a nonparametric multivariate standardized drought index across the Yellow River basin, China

Accepted Manuscript Drought structure based on a nonparametric multivariate standardized drought index across the Yellow River basin, China Shengzhi Huang, Qiang Huang, Jianxia Chang, Yuelu Zhu, Guoyong Leng, Li Xing PII: DOI: Reference:

S0022-1694(15)00725-8 http://dx.doi.org/10.1016/j.jhydrol.2015.09.042 HYDROL 20733

To appear in:

Journal of Hydrology

Received Date: Revised Date: Accepted Date:

5 June 2015 15 September 2015 16 September 2015

Please cite this article as: Huang, S., Huang, Q., Chang, J., Zhu, Y., Leng, G., Xing, L., Drought structure based on a nonparametric multivariate standardized drought index across the Yellow River basin, China, Journal of Hydrology (2015), doi: http://dx.doi.org/10.1016/j.jhydrol.2015.09.042

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1

Drought structure based on a nonparametric multivariate

2

standardized drought index across the Yellow River basin,

3

China

4

Shengzhi Huang a1, Qiang Huanga, Jianxia Chang a, Yuelu Zhua, Guoyong Lengb,

5

Li Xingc

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a State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China

b Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of

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Geographic Sciences and Natural Resources Research, Chinese Academy of

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Sciences, Beijing 100101, China

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c Department of Atmospheric and Oceanic Sciences and Laboratory for Climate and

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Ocean-Atmosphere Studies, School of Physics, Peking University, Beijing 100871,

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China

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18 *Corresponding author at: State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an, 710048, China. Tel.: +86 29 82312801; fax: +86 29 82312797. E-mail Address: huangshengzhi7788@126com. 1

1

Abstract Investigation of drought structure in terms of drought onset, termination,

2

and their transition periods as well as drought duration helps to gain a better

3

understanding of drought regime and to establish a reliable drought early warning

4

system. In this study, a Nonparametric Multivariate Standardized Drought Index

5

(NMSDI) combining the information of precipitation and streamflow was introduced

6

to investigate the spatial and temporal characteristics of drought structure in the

7

Yellow River basin (YRB). Furthermore, the correlations between the El

8

Niño-Southern Oscillation (ENSO) events and NMSDI variations were explored

9

using the cross wavelet technique. The results showed that (1) The variations of

10

NMSDI were consistent with those of 6-month SPI (Standardized Precipitation Index)

11

and SSFI (Standardized Streamflow Index), indicating that the proposed

12

nonparametric multivariate drought index was reliable and effective in characterizing

13

droughts. (2) The preferred seasons of drought onset were spring and summer, and

14

winter was the preferred season of drought recovery in the YRB. The long-term

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average drought duration in the whole basin was nearly 5.8 months, which was clearly

16

longer than the average drought onset and termination transition periods. (3) Overall,

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the drought structure in terms of drought duration, onset and termination transition

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periods in the YRB remained stable, and no appreciable change trend was found. (4)

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ENSO events exhibited a statistically negative correlation with NMSDI variations,

20

suggesting that they showed strong impacts on drought evolutions in the YRB.

21

Although the YRB was selected as a case study in this paper, the approach/indicator

22

can be applied in other regions as well. 2

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Keywords: nonparametric method; integrated drought index; drought structure; cross

2

wavelet analysis; Yellow River basin

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1. Introduction

4

Droughts are naturally recurring hazards that have considerable unfavorable

5

impacts on social and economic development around the world, and their devastating

6

impacts on eco-environmental system are still difficult to estimate (Wilhite, 2000;

7

Mishra and Singh, 2010). Among all types of climate extremes, droughts are one of

8

the costliest and least understood hazards (Wilhite, 2000). It has been reported that

9

droughts led to the largest economic losses in China within the period 1949~1995

10

(Damage Report, 1995). With global warming, the global hydrological cycle is

11

expected to intensify (Alan et al., 2003; Allan and Soden, 2008; Chang et al., 2014),

12

resulting in the increase in extremes such as drought and flood events (Dai, 2011).

13

Given the catastrophic nature of droughts, much attention has being drawn to the

14

drought characteristics at regional and global scales (Wang et al., 2011; Huang et al.,

15

2014a, b; Xu et al., 2014). However, previous studies primarily focused on drought

16

frequency analysis such as drought risk and return period as well as trend and period

17

analysis through various drought indices (Ganguli and Reddy, 2012; Huang et al.,

18

2014a; Bonaccorso et al., 2015). To date, only a few relevant studies have

19

investigated drought structure characteristics in terms of drought onset, persistence

20

and termination (Mo, 2011), which is a major gap in current drought-related

21

knowledge. Because drought occurs slowly, a better understanding of conditions

22

triggering drought onset helps to establish a reliable drought early warning system. If 3

1

appropriate drought triggers are identified, they will substantially improve drought

2

prediction accuracy (Steinemann and Cavalcanti, 2006), which is valuable to regional

3

drought mitigation and water resources management. It is crucial to understand

4

drought persistence characteristics, which have strong effects on the design of water

5

supply systems (Mo, 2011; Bonaccorso et al., 2015). A good understanding of the

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drought persistence characteristics of a specific region is useful for further

7

understanding its drought mechanisms, thus facilitating its agricultural development

8

and drought mitigation. Therefore, it is important to explore the spatial and temporal

9

characteristics of drought structure including the onset, persistence, and recovery of

10

droughts, which helps to fully reveal the drought mechanism and lays a solid

11

foundation for drought prediction.

12

Drought indices used in previous studies, such as the Standardized Precipitation

13

Index (SPI, McKee et al., 1993, 1995), Standardized Streamflow Index (SSFI, Li et al.,

14

2013),Crop Moisture Index (CMI; Palmer, 1968), and Soil Moisture Drought Index

15

(SMDI; Hollinger et al., 1993) embody only one aspect of the shortages of water

16

resources. The current consensus amongst a large number of studies is that developing

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drought indexes based on a single variable/indicator (e.g., precipitation, streamflow,

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or soil moisture) is likely to be insufficient for reliable drought risk assessment and

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reasonable decision-making (Hao and AghaKouchak, 2014). The drought status

20

acquired from one indicator often does not match well with that obtained from a

21

different indicator due to the complex physical interactions among evapotranspiration,

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base flow, direct runoff, infiltration, and groundwater flow. For example, Mo (2011) 4

1

investigated drought onset and recovery over the United States using SPI and soil

2

moisture percentile to characterize meteorological and agricultural droughts,

3

respectively. The evolution characteristics of the onset and termination of

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meteorological drought were found to be different from those of agricultural drought,

5

because the two drought indices are represented by different drought-related variables.

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Therefore, integration of information from multiple sources is urgently required for

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reasonable and reliable drought characterization and prediction, and investigation of

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drought structure based on an integrated drought index combining multivariate

9

information deserves more effort.

10

Most recent drought indices rely on a representative parametric distribution

11

function to fit sample data, and they tend to result in different tail behaviors

12

(Farahmand and AghaKouchak, 2015). In fact, many problems will come up due to

13

the assumption that sample data should follow a given distribution. Note that the

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complicated interactions among surface water, atmosphere, vegetation, soil, and

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groundwater have substantial impacts on hydrologic processes. Thus, any given

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distribution fails to accurately reflect the tail of drought distribution (Sadri and Burn,

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2012). There is no universally accepted parametric distribution for meteorological and

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hydrological variables (Silverman, 1986; Smakhtin, 2001), and the use of a parametric

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distribution tends to result in a remarkable deviation in their low or high quantiles

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(Sharma, 2000). Hence, the application of a parametric drought index in drought

21

assessment is another major gap in current drought-related studies. In this study, a

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nonparametric multivariate standardized drought index (NMSDI) coupled with 5

1

information related to precipitation and streamflow was introduced to investigate the

2

spatial and temporal features of drought structure in the Yellow River basin (YRB),

3

China, without assuming representative parametric distributions.

4

The Yellow River is the second longest river in China and the sixth longest river in

5

the world (Shiau et al., 2007). In northern China, the Yellow River is a major source

6

of freshwater for nearly 107 million residents which account for approximately 8.7%

7

of the total population in China (Wang et al., 2006). The YRB has been heavily

8

plagued by droughts for a long time (She and Xia, 2013). After the 1970s, the

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zero-flow phenomena, which regularly occur in the downstream of the Yellow River,

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have drawn wide attention. The frequently interrupted flow during the past 30 years

11

has led to extremely adverse effects on the social and ecological development in the

12

region. Thus, it is important to reasonably and effectively characterize droughts based

13

on a reliable drought index in the YRB.

14

The primary objectives of this study are: (1) to investigate spatial and temporal

15

characteristics of drought structure in terms of drought onset, persistence and

16

termination as well as their transition periods in the YRB; (2) to determine whether

17

droughts across the YRB have a preferred season to start or end, and to determine the

18

precursors of drought onset or termination; (3) to capture the correlations between the

19

El Niño-Southern Oscillation (ENSO) events and NMSDI variations, along with their

20

evolutionary characteristics in the YRB. Although the YRB was selected as a case

21

study in this paper, the approach/indicator can be applied in other regions as well.

22

2. Study area and data 6

1

2.1 The Yellow River basin (YRB)

2

Fig. 1 shows the study area of this paper, the Yellow River basin (YRB), which is

3

located between 95°E-119°E and 32°N-41°N. The Yellow River originates from the

4

Qinghai-Tibet Plateau in the western portion of China. It first flows northward, turns

5

south, then flows eastward, and finally discharges into the Bohai Sea. The total length

6

of the Yellow River is approximately 5464 km, with a drainage area of 752443 km2.

7

As Chinese ancestors have lived in this basin since prehistoric times, the Yellow

8

River has always been called as the ‘Mother River of China’ (Fu et al., 2004). It

9

should be mentioned that the Chinese Loess Plateau where water loss and soil erosion

10

is extremely severe is situated in the middle of the YRB. Every year, approximately

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1060 million tons of sediment is transported from the Loess Plateau to the Bohai Sea

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(Milliman and Meade, 1983). The climate of the YRB is influenced by the arid and

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semiarid continental monsoon (Wu et al., 2013). Annual precipitation in the YRB

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varies from 123 to 1021 mm, and annual pan evaporation ranges from 700 and 1800

15

mm (Shao et al., 2006). The mean annual precipitation is approximately 378 mm,

16

which increases from the northwest to the southeast in the YRB (Wu et al., 2013).

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Due to the different climate types and topographies in the YRB, the precipitation

18

distribution exhibits a noticeable regional discrepancy. To systematically investigate

19

the characteristics of drought structure in the YRB, the whole basin was divided into

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eight sub-basins on the basis of the secondary basin boundary in China, and their zone

21

numbers are 26, 28, 29, 31, 33, 36, 40, and 41, respectively (Fig. 1). The basin

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boundary map was obtained from the Nanjing Institute of Geography and Limnology, 7

1

Chinese Academy of Sciences

2

(http://lake.geodata.cn/Portal/metadata/viewMetadata.jsp?id=210008-10263), and it

3

was well used in our previous studies (Huang et al., 2015).

4

2.2 Data

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The observed gridded monthly precipitation and simulated monthly runoff data

6

from 1953 to 2012 based on the Variable Infiltration Capacity (VIC) model in the

7

YRB were employed for analysis in this study. The VIC model (Liang et al., 1994) is

8

a semi-distributed macro-scale hydrologic model characterized by representing

9

sub-grid variability in precipitation, soil moisture storage capacity, topography,

10

vegetation classes, etc. (Liang et al., 1994; Nijssen et al., 1997). Meteorological

11

forcing (e.g., wind speed, precipitation, and temperature) for driving the VIC model

12

was obtained from China Meteorological Administration (CMA), which was

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interpolated into 0.25 degree grid. The meteorological forcing obtained from CMA

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includes gauge-based observations (http://www.cma.gov.cn/2011qxfw/2011qsjgx/).

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Approximately 765 meteorological stations are available across the country, in which

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90 stations are located in the YRB. Land surface features, such as vegetation, soil, and

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elevation, were acquired from Nijssen et al. (2001). Six parameters, i.e., the

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infiltration parameter b, the second and third soil layer depths (d2, d3), and the three

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parameters in the baseflow scheme (Dm, Ds, Ws), were calibrated to match the

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long-term monthly runoff observations. The simulations are described in detail by

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Zhang et al. (2014). In addition, the Nino 3.4 Index data covering 1953-2012 were

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utilized to reveal the correlation between ENSO events and NMSDI variations. They 8

1

were obtained from the NOAA Earth System Research Laboratory

2

(http://www.esrl.noaa.gov/psd/data/correlation/nina34.data).

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3. Methodology

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3.1 Nonparametric Multivariate Standardized Drought Index

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For the original SPI, the two-parameter gamma distribution is commonly adopted

6

to fit the probability distribution of precipitation. The cumulative gamma probability

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is then converted into the Cumulative Distribution Function (CDF) of the standard

8

normal distribution. The SPI value can be obtained through calculating the inverse of

9

the standard normal distribution (Huang et al., 2014b). In general, for the calculation

10

of SPI, a mixed distribution is fitted with monthly precipitation data, which are

11

combined a gamma distribution (for non-zero precipitation) and the zero precipitation

12

probability. Then, the SPI value is obtained by the inverse normal transformation of

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the CDF with zero mean and unit variance. Similarly, the calculation of SSFI is

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similar to that of SPI, and the Pearson III distribution is employed to obtain SSFI time

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series in this study (Li et al., 2013). As parametric methods have some limitations in

16

constructing drought indices, the empirical probability that is distribution-free can

17

replace them to derive a nonparametric standardized index. Because the detailed

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calculation processes of NMSDI are well introduced in Farahmand and AghaKouchak

19

(2015), they are omitted in this study for the sake of brevity.

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3.2 Drought onset and termination

9

1

For a specific area, the drought event is identified when the NMSDI index is below

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a given threshold for the duration T defined as a time period more than 3 months. The

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onset month To is the first month when the index is below the threshold. The

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termination month Tt is the first month when the index is above the threshold. The

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threshold for drought onset is -0.8 for the NMSDI index (Hao and AghaKouchak,

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2013a, b). To make sure that this area has adequately recovered from drought, the

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threshold for termination is defined as -0.2 (Mo, 2011). The number of months when

8

NMSDI is negative before this area is recognized as under drought can be regarded as

9

the transition period resulting in the drought onset (No, for the sake of brevity, which

10

is hereafter referred to as the onset transition period), which is defined as the

11

continuous period from the dry month (i.e. NMSDI<0) to the month corresponding to

12

drought onset (i.e., NMSDI = -0.8). The onset transition period varies from one

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drought to another. If the average onset transition period is long, water resource

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managers can utilize this information to mitigate the adverse influence of drought

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during the transition period. Similarly, the transition period resulting in the drought

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termination Nt is defined as the continuous period from the month corresponding to

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the drought onset (i.e. NMSDI=-0.8) to the first month where NMSDI<-0.2. The

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drought duration (Td) is defined as the number of months between the onset month

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and the termination month. The drought onset transition period, duration, and

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termination transition period are critical components of droughts. Therefore, fully

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revealing their spatial and temporal characteristics helps to further understand drought

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mechanisms, thereby facilitating regional drought mitigation. 10

1

2

3.3 The modified Mann-Kendall (MMK) trend test method

The original Mann-Kendall (MK) trend test approach recommended by the World

3

Meteorological Organization (Mitchell et al., 1966) is a nonparametric method for

4

calculating the change trend of a given time series. However, the results of the MK

5

trend test method are expected to be affected by the persistence of time series. Hamed

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and Rao (1998) provided a modified Mann-Kendall (MMK) trend test method

7

through taking the lag-i autocorrelation into account to remove the persistence.

8

Daufresne et al. (2009) stated that the MMK trend test method was more robust than

9

MK in computing the trends of hydro-meteorological series. Therefore, MMK was

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used in this study to calculate the change trends of drought structure in the YRB.

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For a time series of n observations X = x1 ,x2 ,...,xn , the statistic S of MK is

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calculated as follows: S = ∑ sgn( x j − xi )

13

(1)

i< j

14

15

16 17

where

 1 x j > xi  sgn( x j − xi ) =  0 x j = xi   −1 x j < xi

(2)

The variance of S is computed as follows: Var ( S ) =

n ( n − 1)(2 n + 5) 18

11

(3)

1

Then, the standardized test statistic Z =

S with the standard normal variate Var ( S )

2

under the desired confidence level is used to test the significance of the trend of the

3

time series. Hamed and Rao (1998) stated that the significant temporal

4

autocorrelations would impact the evaluation of the variance of S. To remove the

5

effect of the persistence, Hamed and Rao (1998) suggested extracting a nonparametric

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trend estimator from the original time series X and to estimate the autocorrelation of

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the new time series. Autocorrelation coefficients ( ρs(i ) at lag (i)) that are

8

significantly different from zero at the 95% confidence level are then utilized to

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estimate the modified variance of S and V∗( S) which is expressed as follows:

V ∗( S ) = Var( S )Cor

10 11

where Cor is a correction due to the autocorrelation of the time series, which is

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calculated as follows:

13

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Cor = 1+

n−1 2 (n −1)(n − i −1)(n − i − 2)ρS (i) ∑ n(n −1)(n − 2) i =1

(4)

(5)

3.4 The cross wavelet analysis

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The cross wavelet analysis is a new technique coupled with the wavelet transform

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and cross spectrum analysis. It can preferably capture the change characteristics and

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coupled oscillations of two time series both in time and frequency domains, thereby

18

fully revealing their detailed correlations and evolution characteristics (Hudgins and

19

Huang, 1993; Torrence and Compo, 1998). Note that ENSO events are closely

20

associated with drought and flood patterns in various regions around the globe, and

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they have strong influences on climate at regional and global scales via

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teleconnections (Glantz et al., 1991). Wang et al. (2001) noted that ENSO events are 12

1

closely associated with decreased rainfall in the source regions of the Yellow River.

2

Therefore, the correlations between ENSO events and NMSDI variations and their

3

evolution characteristics are explored in this study, which is expected to help reveal

4

the causes of droughts and the establishment of a reliable drought early warning

5

system based on the information related to large-scale circulation pattern. The specific

6

calculation processes of the cross wavelet analysis can be referred to Torrence and

7

Compo (1998), and the relevant codes can be freely downloaded from the following

8

website: http://www.pol.ac.uk/home/research/waveletcoherence/.

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4. Results and discussion

10 11

4.1 The performance of the NMSDI The NMSDI series of each sub-basin in the YRB was computed. To examine the

12

performance of the developed NMSDI, their corresponding 6-month SPI and SSFI

13

series were calculated and compared with NMSDI. Note that precipitation and

14

streamflow with different time scales may be more related to each other than those at

15

a common 6-month scale in snow-dominated regions, which depends on their climate

16

and underlying surface characteristics. In the study area, only sub-basin 41, located in

17

the source of the Yellow River, is a snow dominated region. To determine whether

18

6-month precipitation is more correlated with 3-month runoff than that with 6-month

19

runoff in this region, the correlation coefficients between 6-month precipitation and

20

3-month/6-month runoff in sub-basin 41 were calculated. The correlation coefficient

21

between 6-month precipitation and 6-month runoff is 0.966, whereas that between

22

6-month precipitation and 3-month runoff is only 0.644, which is clearly lower. This 13

1

result indicates that 6-month precipitation is more correlated with 6-month runoff than

2

with 3-month runoff in sub-basin 41. Therefore, it is reasonable to use 6-month

3

precipitation and 6-month runoff data to develop an integrated drought index in this

4

study. For a better visual comparison, the NMSDI, SPI, and SSFI series spanning

5

1993-2012 in sub-basin 31 were plotted and presented in Fig. 2.

6

In general, the variations of NMSDI series in sub-basin 31 are consistent with those

7

of 6-month SPI and SSFI, which demonstrates the reliability and effectiveness of the

8

nonparametric method in characterizing wet and dry conditions. This finding is

9

consistent with Farahmand and Aghakouchak (2015) who stated that the NMSDI was

10

a statistically consistent drought index based on different drought-related variables.

11

As shown in Fig. 2, the performance of NMSDI in capturing drought onset is similar

12

to that of SPI, and that the performance of NMSDI in determining drought persistence

13

and termination is similar to that of SSFI. Because NMSDI is derived from the

14

combined information of precipitation and streamflow, it is more sensitive than SPI or

15

SSFI in capturing the onset, persistence, and termination of droughts, and its

16

identification results are more reliable. The same patterns of NMSDI, SPI, and SSFI

17

are observed in other sub-basins in the entire period. For brevity, the related figures

18

are omitted. In view of the comprehensiveness and effectiveness of NMSDI in

19

characterizing drought, it was adopted in this study to investigate the spatial and

20

temporal characteristics of drought structure in the YRB.

21

4.2 Preferred seasons for drought onset and termination

14

1

Understanding the preferred seasons of drought onset and termination is helpful for

2

regional drought mitigation. In each sub-basin, drought events are identified based on

3

the NMSDI series covering 1953-2012. The ratios of the drought events occurring in

4

and ending in each season to the total number of drought events are illustrated in Fig.

5

3 and Fig. 4, respectively. It can be easily seen from Fig. 3 that the preferred season of

6

the drought onsets in the YRB has a discernable discrepancy ranging from 12% to 48%

7

in the four seasons. At a seasonal scale, drought onsets occurring in spring have the

8

highest frequency, whereas those occurring in winter have the lowest frequency.

9

Overall, the risk of drought onsets occurring in spring and summer is larger than that

10

occurring in autumn and winter. The YRB is a critically important agricultural region,

11

and most of agricultural activities operate in spring and summer. Therefore, the

12

drought onsets frequently occurring in spring and summer pose a big challenge to

13

regional agricultural development. At the sub-basin scale, both the highest and lowest

14

frequencies of drought onsets occur in sub-basin 41 in spring and autumn,

15

respectively.

16

Similarly, the preferred season of drought termination has a noticeable discrepancy

17

ranging from 0 to 46% in the four seasons in the YRB (Fig. 4). The drought

18

terminations occurring in winter have the highest frequency, whereas those occurring

19

in autumn have the lowest frequency. It should be noted that the drought terminations

20

occurring in spring in sub-basin 33 (located in the upstream of the Yellow River) have

21

a high frequency (approximately 45%), whereas the drought termination do not occur

22

in autumn in sub-basin 36 (situated in the downstream of the Yellow River). This 15

1

does not rule out the possibility of the existence of persistent drought or onset of

2

drought in this season in this area, but it suggests that the end of drought never occurs

3

in autumn in sub-basin 36 during the period 1953-2012.

4

4.3 Spatial features of drought structure in the YRB

5

In each sub-basin, drought structure in terms of drought onset and termination

6

transition period as well as drought duration are obtained based on the NMSDI series

7

covering 1953~2012. The spatial distribution of the long-term average drought onset

8

transition period in the YRB is shown in Fig. 5A. The drought onset transition period

9

in the YRB shows a spatial difference ranging from 2.1 to 3.3 months (Fig. 5A).

10

Sub-basin 31 (the Wei River basin) has the longest drought onset transition period,

11

whereas sub-basin 36 has the shortest drought onset transition period. The average

12

drought onset transition period in the whole basin is nearly 2.7 months.

13

The spatial distribution of the average drought termination transition period in the

14

YRB is shown in Fig. 5B. Fig. 5B indicates that the average drought termination

15

transition period of each sub-basin has a noticeable spatial discrepancy ranging from

16

1.9 to 3.1 months in the YRB. The average drought termination transition period in

17

the whole basin is nearly 2.5 months, which is slightly shorter than that of the drought

18

onset transition period. The source of the Yellow River (sub-basin 41) has the longest

19

drought termination transition period (approximately 3.1months), whereas sub-basin

20

40 (located in the downstream of the Yellow River) has the shortest drought

21

termination transition period (nearly 1.9 months). Overall, the drought termination

22

transition period decreases from upstream to downstream in the YRB. 16

1

The spatial distribution of long-term average drought duration in the YRB is shown

2

in Fig. 5C. The drought duration in the YRB ranges from 5 to 6.3 months, and the

3

average drought duration of the whole basin is approximately 5.8 months. The

4

drought duration is so long that it can exert extremely unfavorable impacts on the

5

social and ecological development in this region. Spatially, sub-basin 26 located in the

6

middle of the basin and sub-basin 41 (situated at the source of the Yellow River) have

7

the longest drought duration, whereas sub-basins 31 and 40 (located in the southern

8

and eastern basin) have the shortest drought duration.

9

4.4 Temporal changes in drought structure in the YRB

10

In addition to analyzing the spatial characteristics of drought structure in the YRB,

11

their temporal changes were investigated based on the MMK trend test method

12

outlined in Section 3.3. The autocorrelation coefficients of drought duration, onset

13

and termination transition period in each sub-basin range from -0.5 to 0.5, depending

14

on various sub-basins. For the sake of brevity, only those in sub-basins 33 and 41

15

were plotted and shown in the supplementary materials. The trends of drought

16

duration, onset and termination transition period in each sub-basin are presented in

17

Table 1. Table 1 shows that the drought structure in terms of drought duration, onset

18

and termination transition period in the YRB stays stable with no significant change

19

trend except for sub-basin 33 (located in the upstream of the Yellow River), where a

20

statistically significant decreasing trend at the 95% confidence level was observed.

21

These results are different from those from Damberg and AghaKouchak (2014), who

22

reported that a non-significant trend of drought was found over land in the Northern 17

1

Hemisphere. This difference can be attributed to the different spatial scales and data

2

used in the two studies. Damberg and AghaKouchak (2014) is a global-scale study

3

based on satellite gauge-adjusted precipitation observations, whereas the present study

4

is a regional-scale study based on an integrated drought index combining precipitation

5

and streamflow.

6

4.5 The correlations between ENSO events and NMSDI series in the YRB

7

ENSO events show strong association with drought and flood events in different

8

regions around the globe, and they exert strong influences on climate at both local and

9

regional scales (Glantz et al., 1991). Studying the correlations between ENSO events

10

and droughts, along with their evolutionary characteristics, helps to reveal the causes

11

of droughts in a specific area, which is important for drought mitigation and water

12

resources management in the area. Thus, the cross wavelet analysis was applied to

13

reveal the correlations between ENSO events and NMSDI variations and their

14

evolution characteristics in sub-basins 41, 31, and 36, which are located in the

15

upstream, midstream, and downstream of the Yellow River, respectively. Their cross

16

wavelet transforms are shown in Fig. 6. ENSO events have a statistically negative

17

correlation with NMSDI variation in the upstream of the Yellow River with a 3-5 year

18

signal in 1953-1957, a 2-5 year signal in 1963-1975, and a 2-6 year signal in

19

1986-2000 at the 95% confidence level (Fig. 6A). These statistically significant

20

negative correlations directly demonstrate that ENSO events play an important role in

21

triggering droughts in the YRB.

18

1

Similarly, Fig. 6B indicates that ENSO events exhibit a statistically significant

2

negative correlation with NMSDI variations in the midstream of the YRB at the 95%

3

confidence level with a 2-3 year signal in 1962-1968 and a 4-6 year signal in

4

1982-1991. The statistically significant negative association between the Nino 3.4

5

Index and NMSDI variations in the middle basin also suggests that ENSO events are

6

closely related to droughts in this area.

7

It can be observed from Fig. 6C that ENSO events show a statistically significant

8

negative correlation with NMSDI variations in the downstream of the YRB at the 95%

9

confidence level with a 5-6 year signal in 1980-1993. Additionally, ENSO events also

10

have a statistically significant positive correlation with NMSDI series in this area at

11

the 95% confidence level with a 5-8 year signal in 1955-1966 and a 2-4 year signal in

12

1987-1992, implying that ENSO events are closely associated with droughts in the

13

downstream of the Yellow River. Generally, ENSO events have strong impacts on

14

inducing droughts in the YRB.

15

Because the developed NMSDI is combined with precipitation and streamflow, the

16

relationships between ENSO events and NMSDI variations are impacted by both

17

climate change and human activities. As the major objective of this study is to reveal

18

the drought structure characteristics in the YRB through a reliable integrated drought

19

index, the quantitative analysis of the impacts of climate change and human activities

20

on the associations between ENSO events and NMSDI variations will be conducted in

21

the future study.

22

5. Conclusions 19

1

Investigation of drought structure in terms of drought onset, termination, and their

2

transition periods as well as drought duration, helps to gain a better understanding of

3

drought mechanisms and to establish a reliable drought early warning system. A

4

drought index based on an individual variable may not be sufficient for reflecting

5

drought conditions timely and reliably. Moreover, using parametric methods to

6

construct drought indices leads to different tail behaviors. This study introduced a

7

Nonparametric Multivariate Standardized Drought Index (NMSDI) combining the

8

information of precipitation and streamflow, which is distribution-free and can

9

overcome the limitations of existing parametric approaches. The MMK trend test

10

method was used to obtain the temporal change characteristics of drought structure in

11

the YRB. Furthermore, the cross wavelet analysis was applied to reveal the detailed

12

correlations between ENSO events and NMSDI variations as well as their evolution

13

characteristics. The primary conclusions are as follows:

14

(1) The variations in NMSDI are consistent with those of 6-month SPI and SSFI,

15

which demonstrates the reliability and effectiveness of the nonparametric approach in

16

monitoring wet and dry conditions. Overall, the performance of NMSDI in capturing

17

drought onset is similar to that of SPI, and the performance of NMSDI in determining

18

drought persistence and termination is similar to that of SSFI. Thus, it is an effective

19

index for drought monitoring and prediction.

20

(2) The preferred seasons of drought onset are spring and summer, whereas the

21

preferred season of drought recovery is winter. The drought onset frequently

20

1

occurring in spring and summer poses a major challenge to the agricultural

2

development of the YRB.

3

(3) The long-term average drought onset transition period in the YRB is nearly 2.7

4

months, whereas the long-term average drought termination transition period is

5

approximately 2.5 months. The long-term mean drought duration is nearly 5.8 months

6

which is clearly longer than the drought onset and termination transition periods in the

7

YRB. Generally, the drought structure in terms of drought duration, drought onset and

8

termination transition periods in the YRB remain stable, and no appreciable change

9

trend is detected.

10

(4) ENSO events have statistically significant negative dependence with NMSDI

11

variations, suggesting that they play an important role in the evolution of drought in

12

the YRB.

13

Although the YRB was selected as a case study in this paper, the

14

approach/indicator can be applied in other regions as well.

15

Acknowledgements

16

This research was supported by the Key Innovation Group of Science and

17

Technology of Shaanxi (2012KCT-10), the National Department Public Benefit

18

Research Foundation of Ministry of Water Resources (201501058), the National

19

Major Fundamental Research Program (2011CB403306-2), the National Natural Fund

20

Major Research Plan (51190093), the Natural Science Foundation of China

21

(51179148, 51179149, and 51309188), the Country China Scholarship

22

(201408610067), and China Postdoctoral Science Foundation (2015M570139). 21

1

References

2

AghaKouchak, A., 2014. A Multivariate Approach for Persistence-Based Drought Prediction:

3

Application to the 2010-2011 East Africa Drought. Journal of Hydrology 526, 127-135.

4

Alan, D.Z., Justin, S., Edwin, P.M., Bart, N., Eric, F.W., Dennis, P.L., 2003. Detection of

5

intensification in global- and continental-scale hydrological cycles: temporal scale of evaluation. J.

6

Clim. 16, 535-547.

7 8 9 10 11

Allan, R.P., Soden, B.J., 2008. Atmospheric warming and the amplification of precipitation extremes. Science 321 (5895), 1481-1484. Bonaccorso, B., Peres, D.J., Castano, A., et al., 2015. SPI-Based Probabilistic Analysis of Drought Areal Extent in Sicily. Water Resources Management 29(2), 459-470. Chang, J.X., Wang, Y.M., Istanbulluoglu, E., et al., 2014. Impact of climate change and human

12

activities on runoff in the Weihe River Basin, China. Quaternary International, in press.

13

http://dx.doi.org/10.1016/j.quaint.2014.03.048

14 15 16 17

Damage Report, 1995. Report of the damage caused by disaster in China. China Statistical Press, Beijing (in Chinese). Damberg, L., AghaKouchak, A., 2014. Global trends and patterns of drought from space. Theoretical and Applied Climatology, 117(3-4), 441-448.

18

Daufresne, M., Lengfellner, K., Sommer, U., 2009. Global warming benefits the small in aquatic

19

ecosystems. Proceedings of the National Academy of Sciences USA 106 (31), 12788-12793.

20

Farahmand, A., AghaKouchak, A., 2015. A generalized framework for deriving nonparametric

21 22 23 24 25 26 27 28 29 30 31 32 33

standardized drought indicators. Advances in Water Resources 76, 140-145. Fu, G.B., Chen, S.L., Liu, C.M., et al., 2004. Hydro-climatic trends of the YRB for the last 50 years. Clim Change 65(1), 149-178. Ganguli, P., Reddy, M.J., 2012. Risk Assessment of Droughts in Gujarat Using Bivariate Copulas. Water Resour Manage (2012) 26, 3301-3327. Glantz, M.H., Katz, R.W., Nicholls, N., 1991. Teleconnections linking World Wide Climatic Anomalies. Cambridge University Press, Cambridge, UK. Hamed, K.H., Rao, A.R., 1998. A modified Mann–Kendall trend test for autocorrelated data. Journal of Hydrology 204, 182-196. Hao, Z.C., Aghakouchak, A., 2013a. A Nonparametric Multivariate Multi-Index Drought Monitoring Framework. J. Hydrometeor, 15, 89-101. Hao, Z.C., Aghakouchak, A., 2013b. Multivariate Standardized Drought Index: Aparametric multi-index model. Advances in Water Resources, 57, 12-18. 22

1

Hollinger, S.E., Isard, S.A., Welford, M.R., 1993. A New Soil Moisture Drought Index for Predicting

2

Crop Yields. In: Preprints, Eighth Conf. on Applied Climatology, Anaheim, CA, Amer. Meteor. Soc.,

3

pp. 187-190.

4

Huang, S.H., Hou, B.B., Chang, J.X., et al., 2014a. Copulas-based probabilistic characterization of the

5

combination of dry and wet conditions in the Guanzhong Plain, China. Journal of Hydrology 519,

6

3204-3213.

7 8

Huang, S.H., Chang, J.X., Huang, Q., et al., 2014b. Spatio-temporal Changes and Frequency Analysis of Drought in the Wei River Basin, China. Water Resources Management 28(10), 3095-3110.

9

Huang, S.Z., Chang, J.X., Leng, G.Y., Huang, Q., 2015. Integrated index for drought assessment based

10

on variable fuzzy set theory: a case study in the Yellow River basin, China. Journal of Hydrology,

11

527, 608–618.

12 13 14 15 16

Hudgins, L., Friehe, C.A., Mayer, M.E., 1993. Wavelet transforms and atmospheric turbulence. Phys. Rev. Lett. 71, 3279-3282. Liang, X., Lettenmaier, D.P., Wood, E.F., et al. 1994. A simple hydrologically based model of land surface water and energy fluxes for GSMs. J Geophys Res 99, 14415-14428. Li, S., Xiong, L.H., Dong, L.H., et al., 2013. Effects of the Three Gorges Reservoir on the hydrological

17

droughts at the downstream Yichang station during 2003–2011. Hydrological Processes 27,

18

3981-3993.

19

McKee, T.B., Doesken, N.J., Kleist, J., 1993. The Relationship of Drought Frequency and Duration to

20

Time Scales, Paper Presented at 8th Conference on Applied Climatology. American Meteorological

21

Society, Anaheim, CA.

22

McKee, T.B., Doesken, N.J., Kleist, J., 1995. Drought Monitoring with Multiple Time Scales, Paper

23

Presented at 9th Conference on Applied Climatology. American Meteorological Society, Dallas,

24

Texas.

25 26

Milliman, J.D., Meade, R.H., 1983. World-wide delivery of river sediment to the oceans. Journal of Geology 91, 1-21.

27

Mishra, A.K., Singh, V.P., 2010. A review of drought concepts. Journal of Hydrology 391, 202-216.

28

Mitchell, J.M., Dzerdzeevskii, B., Flohn, H., 1966. Climate Change, WHO Technical Note 79. World

29

Meteorological Organization, Geneva, pp 79.

30

Mo, K.C., 2011. Drought onset and recovery over the United States, J. Geophys. Res., 116, D20106.

31

Nijssen, B., Lettenmaier, D.P., Liang, X., et al. 1997. Streamflow simulation for continental-scale river

32 33 34

basins. Water Resour Res 33, 711-724. Nijssen, B., Schnur, R., Lettenmaier, D.P., 2001. Global retrospective estimation of soil moisture using the Variable Infiltration Capacity land surface model, 1980-93. J Clim 14, 1790-1808. 23

1 2 3 4 5 6 7 8 9 10 11 12

Palmer, W.C., 1968. Keeping track of crop moisture conditions, nationwide: the new crop moisture index. Weatherwise 21, 156-161. Sadri, S., Burn, D.H., 2012. Nonparametric methods for drought severity estimation at ungauged sites, Water Resources Research 48, W12505. Shao, X.M., Yan, C.R., Wei, H.B., 2006. Spatial and temporal structure of precipitation in the YRB based on Kriging method. Chin J Agrometeorol 27(2), 65-69 (in Chinese). Sharma, A. 2000. Seasonal to interseasonal rainfall probabilistic forecasts for improved water supply management: Part 3-A nonparametric probabilistic forecast model. J Hydrol 239, 249-258. She, D.X., Xia, J., 2013. The spatial and temporal analysis of dry spells in the Yellow River basin, China. Stoch Environ Res Risk Assess 27, 29-42. Shiau, J.T., Feng, S., Nadargjah, S., 2007. Assessment of hydrological droughts for the Yellow River, China, using copulas. Hydrological Processes 21, 2157-2163.

13

Silverman, B. W., 1986. Density estimation for statistics and data analysis, Chapman & Hall, London.

14

Smakhtin, V. U., 2001. Low flow hydrology: A review. J. Hydrol., 240, 147-186.

15

Steinemann, A.C., Cavalcanti, L.F.N., 2006. Developing multiple indicators and triggers for drought

16 17 18 19

plans. Journal of Water Resources Planning and Management 132(3), 167-174. Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis, Bull. Am Meteorol Soc 79, 61-78. Wang, D.B., Hejazi, M., Cai, X.M., et al., 2011. Climate change impact on meteorological, agricultural,

20

and hydrological drought in central Illinois, Water Resour. Res., 47, W09527,

21

doi:10.1029/2010WR009845.

22

Wang, G., Shen, Y., Liu, S., 2001. On the characteristics of response of precipitation and runoff to the

23

ENSO events in the source regions of the Yellow River. Journal of Glaciology and Geocryology 23,

24

16-21.

25

Wang, H.J., Yang, Z.S., Saito, Y., et al., 2006. Interannual and seasonal variation of the Huanghe

26

(Yellow River) water discharge over the past 50 years: Connections to impacts from ENSO events

27

and dams. Global and Planetary Change 50, 212-225.

28

Wilhite, D.A., 2000. Drought as a natural hazard: Concepts and definitions, in Drought: A Global

29

Assessment, Hazards Disasters Ser., vol. I, edited by D. A. Wilhite, pp. 3– 18, Routledge, New

30

York.

31 32 33 34

Wu, D., Yan, D.H., Yang, G.Y., et al., 2013. Assessment on agricultural drought vulnerability in the YRB based on a fuzzy clustering iterative model. Nat Hazards 67, 919-936. Wu, H., Hayes, M.J., Hu, Q., 2001. An evaluation of the standardized precipitation index, the China-Z index and the statistical z-score. Int. J. Climatol. 21, 745-758. 24

1

Xu, K., Yang, D.W., Yang, H.B., et al., 2014. Spatio-temporal variation of drought in China during

2

1961–2012: A climatic perspective. Journal of Hydrology 2014, in press.

3

doi:10.1016/j.jhydrol.2014.09.047.

4 5 6 7

Yapo, P.O., Gupta, H.V., Sorooshian, S., 1998. Multi-objective global optimization for hydrologic models. J. Hydrol., 204, 83–97 Zhang, X., Tang, Q., Pan, M., et al. 2014. A long-term land surface hydrologic fluxes and states dataset for China. J Hydrometeor 15, 957-972.

8

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1 2

3 4

Table 1 The trends of drought duration, onset, and termination transition period in the YRB.

Sub-basins

Drought duration

Onset transition period

Termination transition period

Y26 Y28 Y29 Y31 Y33 Y36 Y40 Y41

0.35 -0.52 -0.53 0.20 -2.03* -1.33 0.51 1.31

-0.47 1.27 1.13 -0.88 0.42 -0.42 0.90 0.64

0.77 0.55 0.57 1.45 2.11 -0.30 -0.29 -1.31

Note: ‘*’denotes significance at the 95% confidence level.

5 6

26

1

Highlights

2

A reliable nonparametric multivariate drought index was constructed.

3

The drought structure of the Yellow River basin (YRB) was fully investigated.

4

The preferred seasons of drought onset and recovery in the YRB were found.

5

ENSO events have a strong impact on droughts in the YRB.

6 7

27

1 2

Fig. 1. Location of the YRB and its eight sub-basins.

3 4 5

6 7 8

Fig. 2. Comparison between NMSDI, 6-month SPI and SSFI series spanning 1993-2012 in sub-basin 31 in the YRB.

9

28

1 2 3 4 5 6 7 8 9

Fig. 3. Ratio of the number of drought onsets occurring in a given season to the total number of drought events; a, b, c, and d denote spring, summer, autumn, and winter, respectively.

29

1 2 3

Fig. 4. Ratio of the number of drought terminations occurring in a given season to the total number of drought events; a, b, c, and d denote spring, summer, autumn, and winter, respectively.

30

A

B

C

1 2 3 4

Fig. 5. The spatial distribution of mean drought transition onset (A), termination period (B), and drought duration (C) in the YRB. 31

1

A

B

C

2 3

Fig. 6. The cross wavelet transforms between the Nino 3.4 Index and NMSDI series in sub-basins

4

41 (A), 31 (B), and 36 (C). The 95% significance confidence level against red noise is exhibited as

32

1

a thick contour, and the relative phase relationship is denoted as arrows (with anti-phase pointing

2

left, in-phase pointing right).

33