In order to describe the overall drought status objectively, a copula-based joint deficit index (JDI) was adopted for analyses of drought characteristics in Luanhe River basin. Monthly precipitation data from 1958 to 2011 selected from 26 rain-gauge stations were used for calculating the JDI. The JDI, which encompasses multiple deficit statuses over time scales from 1 to 12 months by using the 12-dimensional empirical copula, is shown to be capable of providing a comprehensive and objective assessment of droughts. In addition, it is demonstrated that both emerging and prolonged droughts can be captured by the JDI. Results of the drought evaluation over the Luanhe River basin indicate that the frequency of drought occurrence generally increases from northwest to southeast, and droughts observed in summer and autumn are more frequent and severe. Compared with the northwestern part of the area, the drought events in the southeast are characterized by longer duration and greater severity. Furthermore, a general tendency of drying is found in the flood season (July to September) over the basin, with significant aggravating trends in the southeastern part. These related drought characteristics could provide valuable information and references for regional mitigation strategies and water resource management.

INTRODUCTION

Drought, considered as the least understood natural hazard, affects many social activities significantly and causes large economic losses (Mishra & Singh 2010; Masud et al. 2015). Drought commonly originates from an intense and persistent deficiency in precipitation (Zargar et al. 2011), but its evaluation, which is controlled by complex physical mechanisms, has different temporal and spatial characteristics (Modarres 2007; Pasho et al. 2011).

Up to now, a variety of drought indices (such as the Palmer drought severity index (Palmer 1965), rainfall anomaly index (Van Rooy 1965), surface water supply index (Shafer & Dezman 1982), standardized precipitation index (SPI) (McKee et al. 1993, 1995), soil moisture drought index (Hollinger et al. 1993), and standardized precipitation evapotranspiration index (Vicente-Serrano et al. 2010)), which are derived from meteorological or hydrological variables, have been established for identifying and assessing droughts. The validity and reliability of the drought index have dominant influences on the effectiveness of a drought monitoring system (Marcella & Eltahir 2008; Barua et al. 2010; Hosseinzadeh Talaee et al. 2014).

Among these drought indices, the SPI proposed by McKee et al. (1993) is the most commonly used owing to its computational simplicity and flexibility. The SPI measures the accumulated precipitation deficits over a given period of time in a probabilistic manner. It not only is statistically comparable across time and space, but also can represent drought conditions at various time scales (Wu et al. 2005; Vicente-Serrano 2006; Zarch et al. 2015).

Byun & Wilhite (1999) highlighted the causes of drought, which can be divided into two kinds, soil dryness and water resource deficiencies in reservoirs or other sources. The amount of short-term precipitation directly affects soil moisture, and long-term precipitation totals mainly have an impact on water stored in other sources. It is thus obvious that drought is a result of the cumulative effects of water shortages over different periods of time; consequently its characteristics in terms of intensity, magnitude and duration vary with the time scale considered. For a drought assessment based on the SPI, a pre-specified time scale is unable to depict the entire drought condition, while inconsistent responses to different time scales will appear and cause confusion. Therefore, it is suggested that multiple SPIs with various time scales should be examined together to capture the overall drought status, combined with historical records and descriptions. Nevertheless, the final examined results are lacking in objectivity and probabilistic properties due to the subjective judgments involved.

On these grounds, Kao & Govindaraju (2010) proposed a joint deficit index (JDI) by using empirical copulas, and indicated that the JDI is capable of providing an objective description of the overall deficit status. Moreover, Mirabbasi et al. (2013) used the JDI for an evaluation of drought conditions in the northwest of Iran, further showing the robustness and flexibility of this index. The JDI serves as a probability-based drought index that can be constructed from the dependence structures of SPIs with time scales varying from 1 to 12 months. There seems to be a consensus that the SPI at a shorter time scale (1–3 months) is used for detecting meteorological or agricultural droughts, while the SPI on longer time scales (e.g. 6 and 12 months) well represents hydrological and water resources droughts (McKee et al. 1995; Vicente-Serrano & López-Moreno 2005; Mishra & Singh 2010). Hence, the JDI, which determines joint deficit status through the joint cumulative probability of SPIs, can offer an objective and overall measure of drought conditions.

The Luanhe River basin, located in north China, is of great importance for water supply to Tianjin city. Several drought-related studies have been undertaken over the basin, indicating more frequent drought events which have caused diminished water resources availability in recent decades (e.g. Li & Feng 2007; Wang et al. 2015a). Therefore, understanding and qualifying drought occurrence and its spatio-temporal characteristics is of particular importance for the development of adequate mitigation strategies. Although various drought indices have been used for drought monitoring and assessment in the Luanhe River basin, remarkable differences are observed in the results based on different indices (e.g. Ma et al. 2013; Wang et al. 2015b). The emergence of inconsistent results would lead to confusion in making informed decisions on a regional scale, and to some extent become an obstacle to establishing an effective monitoring and forecasting system. It is thus necessary to perform an objective assessment of the overall drought condition based on a statistical drought index, straightforwardly providing an overall concise picture of drought status in the region.

According to Kao & Govindaraju (2010), the computation of JDI requires only precipitation time series with a 50-year minimum recording length. Moreover the JDI, simply the standard normal values, are climatologically consistent for any location. As for the Luanhe River basin focused on in this study, 54-year monthly precipitation data (1958–2011) are available, and precipitation deficit is the main cause of drought in the area, accordingly showing the applicability of the JDI method for this area. This study aims to analyze the drought characteristics in the Luanhe River basin using the JDI approach, expecting to provide valuable information for water resources planners and policy makers.

STUDY AREA AND DATA

The focus of this study is on the Luanhe River basin, which is located in the northern part of the Haihe River basin, China. The basin is between 115 °30′ and 119 °15′E longitude and 39 °10′ and 42 °30′N latitude covering an area of 33,700 km2. Its northwestern and central parts consist of mountains, while the southeast area is mainly flat. The mean annual precipitation in the basin varies from less than 400 mm in the northwest, to more than 700 mm in the southeast, and 70–80% of annual precipitation occurs from June to September. The region has a typical temperate continental monsoon climate, with a mean annual temperature of −0.3 to 11 °C. The mean annual pan evaporation over this area is 950–1,150 mm, while its mean annual actual evaporation is around 350 mm.

The Luanhe River basin was planned to provide a billion cubic meters of water per year to Tianjin city, the largest coastal city open to international trade in north China. However, due to rainfall reduction and soil and water conservation, the average annual runoff of the basin decreased by 30% after 1980 (Li & Feng 2007). Additionally, in the 21st century the consecutive droughts in the basin caused a serious insufficiency of water supplying Tianjin city, consequently aggravating environmental degradation and the water crisis. With the study area serving as an important water supply source, the occurrence and evaluation of drought there play a significant role in the social and economic development of Tianjin city.

Monthly precipitation records were collected from 26 rain-gauge stations regularly distributed throughout the Luanhe River basin (Figure 1). The precipitation series are available from January 1958 to December 2011, with a few missing values that were filled by applying linear regression (Vicente-Serrano 2006). The datasets were originally provided by the Hydrology and Water Resource Survey Bureau of Hebei Province. The location, elevation and annual average precipitation for each selected station are listed in Table 1.
Table 1

Detailed information on the 26 rain-gauge stations

Station Location Elevation (m) Precipitation* (mm) Station Location Elevation (m) Precipitation* (mm) 
Yuershan 116 °10′ E, 41°41′ N 1,530 368.42 Xinglong 117°29′ E, 40°25′ N 620 525.46 
Yudaokou 116°58′ E, 42°02′ N 1,400 420.33 Qijia 118°06′ E, 41°27′ N 610 539.02 
Zhenglanqi 116°01′ E, 42°11′ N 1,360 355.10 Pingquan 118°42′ E, 40°59′ N 540 522.36 
Waigoumenzi 116°37′ E, 41°51′ N 1,250 418.98 Bolounuo 117°18′ E, 41°05′ N 540 513.07 
Baichengzi 116°28′ E, 42°17′ N 1,230 334.30 Xiahenan 117 °42′ E, 41 °18′ N 520 513.22 
Banjieta 117 °30′ E, 41 °52′ N 1,070 449.48 Hanjiaying 117 °50′ E, 40 °56′ N 490 502.35 
Goutaizi 117 °05′ E, 41 °33′ N 980 472.33 Xiaoxishan 117 °56′ E, 41 °11′ N 490 510.12 
Qipanshan 117 °40′ E, 42 °01′ N 950 465.57 Sandaohezi 117 °42′ E, 40 °58′ N 460 517.88 
Miaogongshuiku 117 °50′ E, 41 °43′ N 940 514.92 Sangou 118 °15′ E, 41 °02′ N 430 524.14 
Jiutun 117 °23′ E, 41 °17′ N 850 521.06 Liying 117 °44′ E, 40 °36′ N 420 637.29 
Xuanjiangyingzi 116 °52′ E, 41 °23′ N 830 502.68 Chengde 117 °56′ E, 40 °58′ N 350 512.01 
Baihugou 117 °26′ E, 41 °34′ N 830 486.68 Xiabancheng 118 °10′ E, 40 °47′ N 350 546.20 
Zhangsanying 117 °45′ E, 41 °34′ N 640 493.18 Kuancheng 118 °30′ E, 40 °37′ N 300 636.81 
Station Location Elevation (m) Precipitation* (mm) Station Location Elevation (m) Precipitation* (mm) 
Yuershan 116 °10′ E, 41°41′ N 1,530 368.42 Xinglong 117°29′ E, 40°25′ N 620 525.46 
Yudaokou 116°58′ E, 42°02′ N 1,400 420.33 Qijia 118°06′ E, 41°27′ N 610 539.02 
Zhenglanqi 116°01′ E, 42°11′ N 1,360 355.10 Pingquan 118°42′ E, 40°59′ N 540 522.36 
Waigoumenzi 116°37′ E, 41°51′ N 1,250 418.98 Bolounuo 117°18′ E, 41°05′ N 540 513.07 
Baichengzi 116°28′ E, 42°17′ N 1,230 334.30 Xiahenan 117 °42′ E, 41 °18′ N 520 513.22 
Banjieta 117 °30′ E, 41 °52′ N 1,070 449.48 Hanjiaying 117 °50′ E, 40 °56′ N 490 502.35 
Goutaizi 117 °05′ E, 41 °33′ N 980 472.33 Xiaoxishan 117 °56′ E, 41 °11′ N 490 510.12 
Qipanshan 117 °40′ E, 42 °01′ N 950 465.57 Sandaohezi 117 °42′ E, 40 °58′ N 460 517.88 
Miaogongshuiku 117 °50′ E, 41 °43′ N 940 514.92 Sangou 118 °15′ E, 41 °02′ N 430 524.14 
Jiutun 117 °23′ E, 41 °17′ N 850 521.06 Liying 117 °44′ E, 40 °36′ N 420 637.29 
Xuanjiangyingzi 116 °52′ E, 41 °23′ N 830 502.68 Chengde 117 °56′ E, 40 °58′ N 350 512.01 
Baihugou 117 °26′ E, 41 °34′ N 830 486.68 Xiabancheng 118 °10′ E, 40 °47′ N 350 546.20 
Zhangsanying 117 °45′ E, 41 °34′ N 640 493.18 Kuancheng 118 °30′ E, 40 °37′ N 300 636.81 

*Annual average precipitation.

Figure 1

Location of the Luanhe River basin and the 26 rain-gauge stations.

Figure 1

Location of the Luanhe River basin and the 26 rain-gauge stations.

METHOD

SPI and JDI

The SPI and the JDI used in this study were originally proposed by Mckee et al. (1993) and Kao & Govindaraju (2010), respectively.

Let P(t) represent the precipitation measured at time tt= 1 month in this study). For a given w-month time scale, the aggregated precipitation Xw(t) with respect to t is expressed as follows: 
formula
1
In order to reduce the degree of auto-correlation among samples and seasonal effects, 12 sub-series Xwm were obtained by dividing the series Xw based on its ending month: 
formula
2
where g = 1, 2, …, n is the year index; m = 1, 2, …, 12 is the month index, representing January, February, … December, respectively.
By fitting a two-parameter Gamma (G2) distribution separately for each group xwm(g), the marginal cumulative distribution functions (CDFs) are constructed, and then the SPIwm can be computed by taking the inverse normal random variables from the cumulative probability values (uwm): 
formula
3
For the specified time scale of w months, the 12 sub-series SPIwm(g) were rearranged into series SPIw(t) based on time t. Drought classifications along with the corresponding SPIw values are listed in Table 2 (Mckee et al. 1995). According to McKee et al. (1993), a drought event is defined as a period in which the SPIw continuously reaches a value of −1.0 or less. In this study, two parameters (including drought duration and magnitude, denoted by D and M, respectively) were used to characterize the drought event. Drought duration (D) is the length of the drought period, and drought magnitude (M) is identified as follows (Mckee et al. 1993): 
formula
4
where i starts with the first month of a drought and continues to increase until the end of the drought (x) for any of the w time scale. M is commonly used for measuring the drought severity; the larger the value, the more severe the drought event.
Considering the strong seasonality of precipitation, time scales from 1, 2, to 12 months (namely w = 1, 2, …, 12) were selected in this study. Thus, a 12-dimensional joint distribution is needed to combine the univariate marginal distributions of each time scale (uwm, w = 1, …, 12). As adopted by Kao & Govindaraju (2010) and Mirabbasi et al. (2013), a 12-dimensional empirical copula function (Equation (5)) was employed to construct a non-parametric joint empirical probability distribution (Nelsen 2006). 
formula
5
where n is the sample size; I(A) denotes the indicator variable of the logical expression A, which assumes a value of 0 if A is false and 1 if A is true; Ri1, … , Ri12 are the ranks of the ith observed data that are represented as u1m, … , u12m, respectively, and uwm are the values of the cumulative probability of Xwm where w = 1,… , 12.
Table 2

Drought classification of SPI and JDI

Drought condition Index value Drought category 
Wet Greater than 1.0 −1 
Normal −0.5 to 1.0 
Mild drought −1.0 to −0.5 
Moderate drought −1.5 to −1.0 
Severe drought −2.0 to −1.5 
Extreme drought Less than −2.0 
Drought condition Index value Drought category 
Wet Greater than 1.0 −1 
Normal −0.5 to 1.0 
Mild drought −1.0 to −0.5 
Moderate drought −1.5 to −1.0 
Severe drought −2.0 to −1.5 
Extreme drought Less than −2.0 

For the given marginal sets {u1m, … , u12m}, the copula measures the cumulative joint probability and, further, the Kendall distribution function Kc can provide the cumulative probability function (Nelsen et al. 2003; Nelsen 2006).

As for the 12-dimensional empirical copula, an empirical distribution function KCn can be used and is given by (Genest et al. 2009; Mirabbasi et al. 2013): 
formula
6
where .
The Kc(q) represents the cumulative probability for events with the joint deficit status less than or equal to the given threshold q. Analogously to SPI, JDI is defined as follows: 
formula
7
Since the JDI is statistically similar to the SPI, the methods of drought classification and definition which are suitable for SPI can be adopted for JDI as well. For more details on calculating the JDI refer to Kao & Govindaraju (2010) and Mirabbasi et al. (2013).

Mann-Kendall trend test

The non-parametric Mann-Kendall (MK) trend test is one of the most widely used methods for detecting trends of hydro-meteorological time series (Mann 1945; Kendall 1975). Compared with other parametric tests, this statistic method is more robust and does not assume normality of data (Lanzante 1996). In the MK trend test, the standardized test statistic Z is used as an estimator; a positive value of Z shows an increasing trend while a negative value shows a decreasing one. The Z can be calculated as follows: 
formula
8
 
formula
9
where x is the variable with the observed time series (x1, … , xn); n is the sample size; the test statistic S is approximately distributed normally when n ≥ 10, with its variance Var(S) = [n(n − 1)(2n + 5)]/18.

Under the null hypothesis H0 that x are independent and randomly ordered, when |Z| > Z1−α/2, the H0 is rejected and a significant trend exists in the time series. Z1−α/2 is the critical value of Z from the standard normal table, and for 10% significance level the value of Z1−α/2 is 1.28.

RESULTS AND DISCUSSION

SPI and JDI

The 1- to 12-month cumulative precipitation series for each month and each station are fitted with a two-parameter Gamma (G2) distribution, using the maximum likelihood (ML) method to estimate parameters of the distribution. The Kolmogorov–Smirnov (KS) test was then applied for the goodness of fit at the 1% significance level. Results show that more than 95% of the cases passed the KS tests, indicating that the G2 distribution is an appropriate distribution for constructing the SPI and JDI in the Luanhe River basin.

Figure 2 illustrates the evolution of 1- and 12-month SPI and JDI during the period 1959–2011 at Chengde station. The SPI1 series with greater fluctuation indicate that the droughts identified at a shorter time scale have higher temporal frequency and shorter durations, while the SPI with a longer time scale (SPI12), varying more smoothly, captures the drought events that are less frequent but lasted longer. As a whole, the JDI series show a similar temporal behavior to the SPI12. Nevertheless, when marked differences exist in the multiple SPIs, the JDI appears to give a better explanation for the drought condition. For example, the period of February 2010 to June 2010, with sufficient precipitation, is assigned to a wet episode according to the SPI1. However, due to the serious water deficit accumulated in earlier months, this period is dominated by moderate drought conditions, evident in the SPI12. The JDI, which is capable of capturing the joint behaviors of SPIs over various time scales, defines the overall deficit status in this period as normal.
Figure 2

SPI1, SPI12 and JDI series at Chengde station.

Figure 2

SPI1, SPI12 and JDI series at Chengde station.

According to historical records and related literature, drought events mainly occurred in 1961, 1963, 1968, 1972, 1980–1984, 1997–2007 and 2009 for the study area. Based on the series of SPI3, SPI6, SPI12 and JDI, the parameters (including drought duration (D) and magnitude (M)) of the above drought events are reported in Table 3, taking Chengde station as an example.

Table 3

Comparison of drought characteristics based on different indices values

  Historical record
 
SPI3
 
SPI6
 
SPI12
 
JDI
 
Main drought event Beginning date Drought condition 
1961 Apr 1961 Extreme drought 4.03 7.12 20 30.32 11.45 
1963 Jul 1963 Severe drought 2.89 8.07 11 15.08 9.11 
1968 Jul 1968 Mild drought 2.55 2.67 
1972 Apr 1972 Extreme drought 4.76 4.42 14 22.7 11.35 
1980–1984 Feb 1981 Severe drought 1.03 4.24 10 10.96 8.82 
Mar 1984 Moderate drought 1.17 3.57 3.44 3.48 
1997–2007 Jul 2000 Extreme drought 5.43 10 12 19.63 14.9 
Jul 2002 Severe drought 4.38 8.27 10 13.19 7.86 
Jul 2006 Moderate drought 7.7 14.46 11 21.23 12.9 
2009 Aug 2009 Severe drought 1.4 4.45 9.58 5.78 
  Historical record
 
SPI3
 
SPI6
 
SPI12
 
JDI
 
Main drought event Beginning date Drought condition 
1961 Apr 1961 Extreme drought 4.03 7.12 20 30.32 11.45 
1963 Jul 1963 Severe drought 2.89 8.07 11 15.08 9.11 
1968 Jul 1968 Mild drought 2.55 2.67 
1972 Apr 1972 Extreme drought 4.76 4.42 14 22.7 11.35 
1980–1984 Feb 1981 Severe drought 1.03 4.24 10 10.96 8.82 
Mar 1984 Moderate drought 1.17 3.57 3.44 3.48 
1997–2007 Jul 2000 Extreme drought 5.43 10 12 19.63 14.9 
Jul 2002 Severe drought 4.38 8.27 10 13.19 7.86 
Jul 2006 Moderate drought 7.7 14.46 11 21.23 12.9 
2009 Aug 2009 Severe drought 1.4 4.45 9.58 5.78 

Note: unit of drought duration (D) is one month.

It can be seen in Table 3 that both SPI and JDI have the ability to identify and assess the historical drought events, but values of the drought parameters defined by these indices are different from each other. Short-term SPI values are more sensitive to emerging droughts, while a long-term SPI value shows a strong response to a prolonged drought. For example, the mild drought starting in July 1968 cannot be captured by the long-term SPI (namely SPI6 and SPI12), while the SPI3 indicates this drought event with a duration of 2 months, which is also suggested by the JDI. In the case of the extreme drought that occurred in 2000, the drought parameters obtained by the multiple SPIs have great differences (e.g. the D and M of SPI12 are four times larger than the corresponding ones of SPI3), but a duration of 8 months defined by the JDI is consistent with the historical record. Among the multiple SPIs, the SPI6 shows better performance in capturing historical drought events in the study area, since the general agreement of its assessment results and historical records seems good. However, when considering the short-term drought in 1968 and the extreme droughts in 1961 and 1972, remarkable differences are exhibited especially in terms of drought magnitude. Compared with the SPI6, the results of JDI are in better agreement with historical records for all the cases listed in Table 3 on the whole. For instance, the extreme drought event that occurred in 1972 lasted 6 months, affecting an area of 30,000 km2 in Chengde city. It was reported to be the most severe drought event since 1919 and caused great damage to the eco-environment and socio-economy in this region (Gao 1998). According to the JDI, the corresponding assessment result with a duration of 6 months and a magnitude of 11.35 replicates this drought condition well. It is indicated that the JDI, which integrates the deficit status over various durations (from 1 to 12 months), can avoid the confusion caused by multiple SPIs with different time scales, and accurately define and assess overall drought conditions.

Four cases with the drought categories based on SPIw (w = 1, 2, …, 12) and JDI, as well as the corresponding 1- to 12-month precipitation, were selected and presented in Figure 3.
Figure 3

Results of drought assessment based on SPI and JDI and the corresponding precipitation for four selected cases.

Figure 3

Results of drought assessment based on SPI and JDI and the corresponding precipitation for four selected cases.

As shown in Figure 3(a), values of SPI at all time scales for June 1972 indicate severe and even extreme drought conditions due to serious precipitation deficits. The JDI that represents the joint deficit status also suggests an extreme drought for this case. In the case of July 1972 (Figure 3(b)), the SPI1 assigned to a wet class shows sufficient precipitation in this month, while the SPIs with other time scales reflect a drought state due to precipitation deficits in prior months. The JDI takes the effect of preceding serious deficits into account, and reports a severe drought in this instance.

For December 1993 (Figure 3(c)), SPI1 reports a severe drought since hardly any precipitation was observed. However, other SPIs with longer memory cannot capture an emerging drought in a timely manner, showing above normal conditions. The JDI indicates a mild drought condition for this instance, demonstrating that the JDI not only can reflect the emerging drought but also has temporal memory for accumulated deficit. Figure 3(d) shows a confusing case in April 2007, in which SPI with time scales from 1 to 5 months show approximately normal precipitation in the last five months, while other SPIs accounting for the preceding serious deficit report drought status with different severity. Based on the entire dependence structure of multiple SPIs, the JDI reflects a mild drought condition in this case.

Figure 4 shows regional illustrations of the drought condition for December 2000 based on SPI1, SPI3, SPI6, SPI9, SPI12 and JDI. According to historical records, the Luanhe River basin suffered widespread drought in 2000, with most areas experiencing severe to extreme droughts especially for the period June to September. Compared with the southeast area, the drought condition in the northwest was more serious and longer lasting. In October and November 2000, sufficient precipitation was observed and hence the short-term preceding deficit seemed to be relieved to some extent. Therefore, for December 2000, the 1- and 3-month SPI indicate that the deficit status has come back to normal overall (Figure 4(a) and 4(b)). At the time scale of 6 and 9 months the drought condition was in its development stage, and SPI6 and SPI9 show more severe precipitation deficits in the southeast (Figure 4(c) and 4(d)). The SPI at the 12-month time scale is expected to involve the accumulated water deficit during the entire duration of drought and determines drought status in most sites (Figure 4(e)), but its longer memory delays the response for the increased precipitation in recent months (October and November). The JDI, which reports normal status in most areas but determines mild to moderate droughts in the central part (Figure 4 (f)), not only reflects the effect of precipitation supply in a timely manner, but also effectively considers the temporal memory for moisture deficit. These results support the conclusion that the JDI is capable of capturing both emerging and prolonged droughts in a timely manner, which is demonstrated by Kao & Govindaraju (2010).
Figure 4

Regional illustration of the drought condition of the study area for December 2000.

Figure 4

Regional illustration of the drought condition of the study area for December 2000.

Drought characteristics based on JDI

The frequency of drought occurrences for each drought category was calculated using JDI, considering the periods of 1959–1969, 1970–1979, 1980–1989, 1990–1999 and 2000–2011, and four seasons (namely, spring (March to May), summer (June to August), autumn (September to November) and winter (December to February)). As an average of the 26 stations, the frequency associated with the mild, moderate, severe and extreme drought expressed as percentages are given in Figures 5 and 6 for different periods and different seasons, respectively.
Figure 5

Frequencies of drought in different years.

Figure 5

Frequencies of drought in different years.

Figure 6

Frequencies of drought for different seasons.

Figure 6

Frequencies of drought for different seasons.

Figure 5 shows that the frequencies related to severe and extreme drought classes generally tend to increase over time, especially in the most recent decade, which is consistent with previous studies (Li & Feng 2007; Wang et al. 2015a). In Figure 6, it can be seen that mild droughts observed during 1959–2011 mostly occurred in the autumn. The maximum frequencies associated with moderate, severe and extreme drought occur in summer, indicating that summer droughts seem to be more frequent and severe.

In the Luanhe River basin, the precipitation in summer and autumn (from June to November) accounts for more than 80% of annual precipitation, predominating in the water budgets of the hydrological cycle. Most of the regional agricultural production is from irrigated agriculture, and the corresponding agricultural activities are concentrated in summer and autumn. Moreover, sufficient precipitation during the flood season (from June to September) serves as a key element for an adequate reservoir storage which directly guarantees the quality of water supply for Tianjin city. Consequently, the severe and frequent droughts in summer and autumn have seriously affected river ecosystems and irrigated agriculture in the basin, resulting in crop failures, water scarcity and environmental degeneration. In the most recent decade, Tianjin city has faced a water crisis due to the inadequate supply of water, as a response to the frequent occurrence of extreme droughts in the Luanhe River basin. It is thus of great significance for the Luanhe River basin to improve drought mitigation strategies and water resources management.

In this study, the non-parametric MK trend test was used to detect the trend of the JDI series during 1959–2011, and the Z statistics of the MK test for each month and each station are listed in Table 4. Based on the Z statistics of the MK test, a positive value shows a mitigating trend of drought condition, while a negative value shows an aggravating trend. In August and September, negative Z values are observed in all the stations, and show significance at the 90% confidence level for the stations located in the southeast. It is indicated that the drought in August and September has an aggravating trend over the basin, shown to be significant in the southeastern part. Z values for July are found to be negative in about 85% of the selected stations, suggesting aggravating trends of drought condition in July. Moreover, more than 50% of the stations show significant aggravating trends in January, February and March droughts, and these stations are mostly located in the southeast. For the drought condition in May and June, positive Z values were found in more than 75% of the stations, reflecting mitigating trends.

Table 4

Z Statistics of MK trend test based on JDI for each month and station in the study area

Station Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 
Yuershan 0.38 0.84 0.75 0.77 0.91 0.86 −0.44 −1.01 −0.92 −0.76 0.45 0.62 
Zhenglanqi 0.43 0.59 0.51 0.50 0.83 0.53 −0.27 −1.54* −1.37* −0.51 0.39 1.02 
Baichengzi 0.37 0.45 0.41 0.43 0.75 0.68 −0.57 −1.16 −1.91* −0.33 0.45 0.75 
Waigoumenzi 0.85 0.92 0.58 0.89 1.03 0.96 −0.39 −0.89 −1.07 −0.81 0.78 1.62* 
Yudaokou 0.44 0.94 0.71 0.62 1.70* 1.04 −0.37 −1.56* −1.07 −0.61 0.38 1.62* 
Goutaizi 1.21 0.87 0.37 0.33 1.23 −0.12 −0.35 −1.48* −0.86 −0.30 −0.61 0.04 
Jiutun −1.49* −2.06* −2.52* 0.18 0.64 0.35 −1.05 −0.84 −1.42* −0.93 −0.85 −0.91 
Xuanjiangyingzi −2.50* −1.66* −2.19* −0.38 0.29 0.32 −0.23 −2.88* −1.34* 0.08 −0.87 −1.17 
Sandaohezi −1.79* −1.50* −1.89* 0.11 0.90 −1.65* −0.75 −1.93* −1.68* −1.14 −0.20 −1.17 
Qipanshan 0.56 0.48 0.59 0.62 0.87 0.75 −0.63 −1.39* −0.75 −0.89 0.45 1.36* 
Miaogongshuiku 0.95 −0.08 0.31 1.51* 1.33* 1.20 0.54 −1.01 −0.51 −0.31 0.19 0.91 
Zhangsanying 0.67 0.11 0.79 1.25 1.51* 0.32 0.64 −0.45 −0.46 0.00 −0.25 −0.02 
Banjieta 0.70 0.79 0.55 −0.61 0.95 0.39 −0.83 −1.20 −0.65 0.27 −0.23 −1.79* 
Baihugou 0.68 0.75 −1.14 0.28 0.94 −0.04 −0.43 −0.87 −1.18 −0.22 −0.03 −0.89 
Xiahenan −0.59 −0.89 −1.19 1.12 2.00* 0.89 −0.93 −0.91 −1.55* −0.61 0.15 −1.06 
Hanjiaying −0.28 −0.69 −1.15 0.60 0.85 0.77 −0.94 −1.55* −0.93 −0.36 0.20 −0.42 
Qijia −1.02 −0.45 −0.69 0.04 1.93* 1.66* 0.01 −0.94 −0.85 0.71 0.96 0.74 
Xiaoxishan −1.54* −0.36 −1.29* 0.38 1.68* 1.17 −0.35 −0.92 −0.75 −0.55 −0.07 −1.17 
Chengde −0.64 −0.77 −1.94* −0.55 −0.51 −1.82* −1.12 −1.49* −1.07 0.11 −0.09 0.22 
Sangou −1.53* −1.60* −2.15* −0.47 1.01 0.69 −0.22 −2.08* −1.31* −0.45 −1.33* −1.96* 
Xinglong −1.48* −1.56* −1.50* −0.30 0.26 0.35 −1.05 −1.36* −1.34* −0.57 −0.38 −1.10 
Liying −0.84 −0.82 −1.25 −0.41 0.81 1.39* −0.31 −1.48* −0.94 −0.35 0.11 −0.36 
Pingquan −0.44 −1.63* −1.43* −0.71 0.05 0.37 −0.05 −1.38* −1.05 −0.41 −0.73 −0.32 
Kuancheng −1.89* −1.96* −1.74* −0.97 1.25 1.17 −1.03 −1.50* −1.04 −1.09 −1.82* −1.04 
Bolounuo −1.47* −1.44* −2.63* −0.67 0.11 0.39 −1.12 −1.66* −2.04* −1.02 −1.14 −0.83 
Xiabancheng −2.28* −1.79* −1.54* −0.91 0.80 −1.91* −1.60* −2.39* −1.30* −0.64 −0.84 −1.30* 
Station Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 
Yuershan 0.38 0.84 0.75 0.77 0.91 0.86 −0.44 −1.01 −0.92 −0.76 0.45 0.62 
Zhenglanqi 0.43 0.59 0.51 0.50 0.83 0.53 −0.27 −1.54* −1.37* −0.51 0.39 1.02 
Baichengzi 0.37 0.45 0.41 0.43 0.75 0.68 −0.57 −1.16 −1.91* −0.33 0.45 0.75 
Waigoumenzi 0.85 0.92 0.58 0.89 1.03 0.96 −0.39 −0.89 −1.07 −0.81 0.78 1.62* 
Yudaokou 0.44 0.94 0.71 0.62 1.70* 1.04 −0.37 −1.56* −1.07 −0.61 0.38 1.62* 
Goutaizi 1.21 0.87 0.37 0.33 1.23 −0.12 −0.35 −1.48* −0.86 −0.30 −0.61 0.04 
Jiutun −1.49* −2.06* −2.52* 0.18 0.64 0.35 −1.05 −0.84 −1.42* −0.93 −0.85 −0.91 
Xuanjiangyingzi −2.50* −1.66* −2.19* −0.38 0.29 0.32 −0.23 −2.88* −1.34* 0.08 −0.87 −1.17 
Sandaohezi −1.79* −1.50* −1.89* 0.11 0.90 −1.65* −0.75 −1.93* −1.68* −1.14 −0.20 −1.17 
Qipanshan 0.56 0.48 0.59 0.62 0.87 0.75 −0.63 −1.39* −0.75 −0.89 0.45 1.36* 
Miaogongshuiku 0.95 −0.08 0.31 1.51* 1.33* 1.20 0.54 −1.01 −0.51 −0.31 0.19 0.91 
Zhangsanying 0.67 0.11 0.79 1.25 1.51* 0.32 0.64 −0.45 −0.46 0.00 −0.25 −0.02 
Banjieta 0.70 0.79 0.55 −0.61 0.95 0.39 −0.83 −1.20 −0.65 0.27 −0.23 −1.79* 
Baihugou 0.68 0.75 −1.14 0.28 0.94 −0.04 −0.43 −0.87 −1.18 −0.22 −0.03 −0.89 
Xiahenan −0.59 −0.89 −1.19 1.12 2.00* 0.89 −0.93 −0.91 −1.55* −0.61 0.15 −1.06 
Hanjiaying −0.28 −0.69 −1.15 0.60 0.85 0.77 −0.94 −1.55* −0.93 −0.36 0.20 −0.42 
Qijia −1.02 −0.45 −0.69 0.04 1.93* 1.66* 0.01 −0.94 −0.85 0.71 0.96 0.74 
Xiaoxishan −1.54* −0.36 −1.29* 0.38 1.68* 1.17 −0.35 −0.92 −0.75 −0.55 −0.07 −1.17 
Chengde −0.64 −0.77 −1.94* −0.55 −0.51 −1.82* −1.12 −1.49* −1.07 0.11 −0.09 0.22 
Sangou −1.53* −1.60* −2.15* −0.47 1.01 0.69 −0.22 −2.08* −1.31* −0.45 −1.33* −1.96* 
Xinglong −1.48* −1.56* −1.50* −0.30 0.26 0.35 −1.05 −1.36* −1.34* −0.57 −0.38 −1.10 
Liying −0.84 −0.82 −1.25 −0.41 0.81 1.39* −0.31 −1.48* −0.94 −0.35 0.11 −0.36 
Pingquan −0.44 −1.63* −1.43* −0.71 0.05 0.37 −0.05 −1.38* −1.05 −0.41 −0.73 −0.32 
Kuancheng −1.89* −1.96* −1.74* −0.97 1.25 1.17 −1.03 −1.50* −1.04 −1.09 −1.82* −1.04 
Bolounuo −1.47* −1.44* −2.63* −0.67 0.11 0.39 −1.12 −1.66* −2.04* −1.02 −1.14 −0.83 
Xiabancheng −2.28* −1.79* −1.54* −0.91 0.80 −1.91* −1.60* −2.39* −1.30* −0.64 −0.84 −1.30* 

*Significant trend at the 90% confidence level.

The spatial distributions of drought frequency, mean drought duration and mean drought magnitude over the period of 1959–2011 are presented in Figure 7. The drought frequency within the basin varies from 38.5% (Liying station located in the south) to 12.7% (Miaogongshuiku station located in the north), showing a highly uneven spatial distribution (Figure 7(a)). In general, the frequency of drought occurrence is increasing from the northwest to the southeast in the study area. As for the mean drought duration and mean drought magnitude (Figure 7(b) and 7(c)), the higher values are observed in the stations which are mainly located in the southeastern part, while the stations with the lower values are located in the northwest, which corresponds to the results of the MK test. The Bolounuo station, with the longest mean duration (6.1 months) and maximum mean magnitude (14.34), lies at the south of the basin. The Yudaokou station in the northwest has the shortest mean duration (2.7 months) and minimum mean magnitude (4.11).
Figure 7

Regional illustration of drought frequency, mean drought duration and mean drought magnitude over the period of 1959–2011 in the Luanhe River basin.

Figure 7

Regional illustration of drought frequency, mean drought duration and mean drought magnitude over the period of 1959–2011 in the Luanhe River basin.

CONCLUSIONS

In this paper, monthly precipitation data from 26 rain-gauge stations over the period of 1958 to 2011 were selected to calculate the JDI. The JDI series were then employed to analyze the drought characteristics in the basin. The main conclusions are summarized as follows.

As a probability-based drought index, the JDI takes the effects of water deficits at various time scales into account, objectively reflecting the overall drought status. Compared with the SPI, the JDI can not only provide a more comprehensive drought assessment, but also characterize drought conditions more accurately. Moreover, the JDI constructed in terms of the joint cumulative probability is able to capture both emerging and prolonged droughts effectively, and is shown to be a flexible and appropriate tool for drought monitoring and assessment.

During the period of 1959–2011, serious drought events mainly occurred in summer and autumn in the Luanhe River basin, and extreme droughts appeared frequently in the most recent decade, seriously hitting the river ecosystems, irrigated agriculture and water supply capacity of the basin. Compared with the northwest in the basin, more severe and frequent droughts are observed in the southeast. In addition, the drought condition over the basin tends to be aggravating in August and September, with significant aggravating trends in the southeast. The occurrence and evaluation of droughts can be objectively described by the JDI, providing valuable information and references for developing regional mitigation strategies and water resources management.

The JDI constructed in this study is purely dependent on precipitation deficits over the time scales of 1 month to 12 months. However, under a drought condition, multiple moisture deficits could be observed in many other hydrologic variables (such as streamflow, soil moisture and reservoir storage), which are also varying with the time and spatial scales considered. Therefore, future studies should detect the dependence structures of these different types of deficits in a systematic manner, so as to construct an inter-variable drought index that is more representative for the joint behavior of regional droughts. Moreover, the drought forecast and risk assessment performed based on the JDI should be the subject of further study.

ACKNOWLEDGEMENTS

This work was financially supported by the National Natural Science Foundation of China (No. 51479130). The authors thank the Hydrology and Water Resource Survey Bureau of Hebei Province for providing the observed precipitation data.

REFERENCES

REFERENCES
Barua
S.
Perera
B. J. C.
Ng
A. W. M.
Tran
D.
2010
Drought forecasting using an aggregated drought index and artificial neural network
.
Journal of Water and Climate Change
1
(
3
),
193
206
.
Byun
H. R.
Wilhite
D. A.
1999
Objective quantification of drought severity and duration
.
Journal of Climate
12
(
9
),
2747
2756
.
Gao
J. H.
1998
Elementary research of the tendency in Chengde's environment development in the past 300 years
.
Arid Zone Research
15
(
2
),
70
74
(in Chinese)
.
Genest
C.
Rémillard
B.
Beaudoin
D.
2009
Goodness-of-fit tests for copulas: a review and a power study
.
Insurance: Mathematics and Economics
44
,
199
213
.
Hollinger
S. E.
Isard
S. A.
Welford
M. R.
1993
A new soil moisture drought index for predicting crop yields
. In:
8th Conference on Applied Climatology
,
Anaheim, CA
.
American Meteorological Society
, pp.
187
190
.
Hosseinzadeh Talaee
P.
Tabari
H.
Sobhan Ardakani
S.
2014
Hydrological drought in the west of Iran and possible association with large-scale atmospheric circulation patterns
.
Hydrological Processes
28
(
3
),
764
773
.
Kao
S. C.
Govindaraju
R. S.
2010
A copula-based joint deficit index for droughts
.
Journal of Hydrology
380
(
1
),
121
134
.
Kendall
M. G.
1975
Rank Correlation Methods
.
4th edn. Charles Griffin
,
London
.
Li
J. Z.
Feng
P.
2007
Runoff variations in the Luanhe river basin during 1956–2002
.
Journal of Geographical Sciences
17
(
3
),
339
350
.
Ma
H. J.
Yan
D. H.
Weng
B. S.
Fang
H. Y. &
Shi
X. L.
2013
Applicability of typical drought indexes in the Luanhe River Basin
.
Arid Zone Research
30
(
4
),
728
734
(in Chinese)
.
Mann
H. B.
1945
Nonparametric tests against trend
.
Econometrica
13
,
245
259
.
McKee
T. B.
Doesken
N. J.
Kleist
J.
1993
The relationship of drought frequency and duration to time scales
. In:
Proceedings of the 8th Conference on Applied Climatology
.
American Meteorological Society
,
Boston
, pp.
179
184
.
McKee
T. B.
Doesken
N. J.
Kleist
J.
1995
Drought monitoring with multiple time scales
. In:
Proceedings of the 9th Conference on Applied Climatology
.
American Meteorological Society
,
Boston
, pp.
233
236
.
Mirabbasi
R.
Anagnostou
E. N.
Fakheri-Fard
A.
Dinpashoh
Y.
Eslamian
S.
2013
Analysis of meteorological drought in northwest Iran using the joint deficit index
.
Journal of Hydrology
492
,
35
48
.
Mishra
A. K.
Singh
V. P.
2010
A review of drought concepts review article
.
Journal of Hydrology (Amsterdam)
391
(
1–2
),
202
216
.
Modarres
R.
2007
Streamflow drought time series forecasting
.
Stochastic Environmental Research and Risk Assessment
21
(
3
),
223
233
.
Nelsen
R. B.
2006
An Introduction to Copulas
.
Springer
,
New York
.
Nelsen
R. B.
Quesada-Molina
J. J.
Rodríguez-Lallena
J. A.
Úbeda-Flores
M.
2003
Kendall distribution functions
.
Statistics & Probability Letters
65
,
263
268
.
Palmer
W. C.
1965
Meteorological Drought
.
US Weather Bureau Tech Paper 45
, pp.
1–58
.
Pasho
E.
Camarero
J. J.
de Luis
M.
Vicente-Serrano
S. M.
2011
Impacts of drought at different time scales on forest growth across a wide climatic gradient in north-eastern Spain
.
Agricultural and Forest Meteorology
151
(
12
),
1800
1811
.
Shafer
B. A.
Dezman
L. E.
1982
Development of a surface water supply index (SWSI) to assess the severity of drought conditions in snow pack runoff areas
. In:
Proceedings of the Western Snow Conference
.
Colorado State University
,
Colorado
, pp.
164
175
.
Van Rooy
M. P.
1965
A rainfall anomaly index independent of time and space
.
Notos
14
,
43
.
Vicente-Serrano
S. M.
Begueria
S.
Lopez-Moreno
J. I.
2010
A multi-scalar drought index sensitive to global warming: the standardized precipitation evapotranspiration index-SPEI
.
Journal of Climate
23
(
7
),
1696
1718
.
Wang
Y. X.
Li
J. Z.
Feng
P.
Hu
T.
2015b
A time-dependent drought index for non-stationary precipitation series
.
Water Resources Management
15
,
1
17
.
Wu
H.
Hayes
M. J.
Wilhite
D. A.
Svoboda
M. D.
2005
The effect of the length of record on the standardized precipitation index calculation
.
International Journal of Climatology
25
,
505
520
.
Zargar
A.
Sadiq
R.
Naser
B.
Khan
F. I.
2011
A review of drought indices
.
Environmental Reviews
19
,
333
349
.