Introduction

Drought is a natural phenomenon and a natural hazard, and it occurs over most parts of the world, even in wet and humid regions (Dai 2011). Based on different disciplinary perspectives, drought can be separated into four categories (Sheffield and Wood 2012): meteorological drought, agricultural drought, hydrological drought, and socioeconomic drought. Among these different types of droughts, the hydrological cycle is the most important given the high dependence of many activities on surface water resources.

Meteorological drought is one of the important factors affecting the hydrological drought (Gumus and Algin 2017). Due to atmospheric transport of anomalously warm and dry air, spatial migration of a drought event from meteorological to hydrological drought would occur (Joseph et al. 2009). It is called “drought propagation.” In addition, propagation of drought is characterized by a number of features, which are related to the fact that the terrestrial part of the hydrological cycle acts as a low-pass filter to the meteorological forcing (Marković and Koch 2005). For example, a prolonged meteorological drought results into hydrological drought, and a lag occurs between meteorological and hydrological droughts. Edossa et al. (2010) analyzed drought characteristics in the Awash River Basin of Ethiopia based on meteorological and hydrological variables, and the results had shown that occurrence of hydrological drought events at Lower Awash lagged meteorological drought events in the upper Awash on average by 7 months. Tabrizi et al. (2010) found that annual time scale of meteorological drought in the upstream of the Doroodzan watershed of Iran can be used to investigate occurrence of streamflow drought in the downstream. Haslinger and Koffler (2014) have explored the linkage between meteorological drought and streamflow. Jörg-Hess et al. (2015) have quantified the effects of quality of meteorological forcing in hydrological droughts. Huang et al. (2016) have investigated the linkages between hydrological drought, climate indices, and human activities in the Columbia River basin. Gumus and Algin (2017) have analyzed the meteorological and hydrological droughts of the Seyhan-Ceyhan River Basin of Turkey. More importantly, the lag of occurring time between meteorological and hydrological droughts is crucial in coping with drought. This time-lag issue has been addressed in some drought-prone regions in Europe and Africa (Hisdal and Tallaksen 2003). This cause-effect relationship between meteorological and hydrological droughts has been modelled with a copula-based joint meteorological-hydrological drought index by Cheraghalizadeh et al. (2018) at upstream and downstream of the Kasilian basin. Huang et al. (2017) have explored the propagation from meteorological to hydrological droughts and identified the potential influence factors. The entropy theory was used by Zhu et al. (2018) to develop a hybrid drought index, which combines meteorological, hydrological, and agricultural information and was applied to investigate the drought condition in Northwest China. Tijdeman et al. (2018) have investigated the natural and human influences on the link between meteorological and hydrological drought indices for a large set of catchments in the contiguous United States.

The standardized precipitation index (SPI) (McKee et al. 1993) and streamflow drought index (SDI) (Nalbantis 2008) are simple and effective indices for meteorological and hydrological droughts, and are also widely used in the literature due to their multiple simultaneous time scales and simplicity of calculation (Ashraf and Routray 2015; Sönmez et al. 2005). Therefore, SPI and SDI were used in this study to calculate the meteorological and hydrological drought events.

The Weihe River is the largest tributary of the Yellow River—the 6th longest river in the world and the “Mother River of China” (Fu et al. 2004), and plays an important role in local economic development (Wei et al. 2012). Its meteorological and hydrological droughts could potentially have a significant effect on regional development. However, it seems there is not a study in the literature to investigate the relationship between meteorological and hydrological droughts in the Weihe River Basin, although a number of study in the literature have documented the hydrological droughts and/or the meteorological drought of Yellow River independently.

The objectives of this paper are to (a) investigate temporal and spatial evolutions of meteorological and hydrological droughts in the Weihe River Basin by using SPI and SDI for 1960–2012 years, (b) investigate the relationships between the meteorological and hydrological droughts including establishing a regression function between the meteorological and hydrological droughts and identifying the lag time between the two droughts, and (c) explore the differences between meteorological and hydrological droughts and discuss the possible reasons.

Study area and data

Study area

As the largest tributary of the Yellow River Basin, the Weihe River Basin of China (Fig. 1), between 103°~110° E and 34°~38° N, originates from north of Niaoshu Mountain in Gansu Province, reaches Tongguan in Shaanxi Province, and flows into the Yellow River. The Weihe River Basin flows 502.4 km long with a drainage area of 134,800 km2 where the well-known Guanzhong Plain in Northwest China is located (Xue et al. 2016). The annual average temperature is about 13.3 °C, annual mean precipitation amounts are in the range of 558–750 mm with a general increasing trend from north to south, and annual mean runoff amounts are 10.37 km3. The runoff from July to September accounts for about 60–70% of annual discharge (Li et al. 2013).

Fig. 1
figure 1

The Weihe River Basin map

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The hydrological regime in the Weihe river basin was heavily affected by human activities, such as increasing population, dams, and irrigation, which could potentially modify the hydrological drought characteristics with the same amount of rainfall (“The Differences between SPI and SDI” section for detailed discussion).

Data sources

The daily precipitation data from 13 standard meteorological stations within the basin were obtained from the China Meteorological Administration (http://cdc.cma.gov.cn) covering the period 1960 to 2012. These stations are from meteorological stations in China with high-quality data, maintained according to standard methods by the National Meteorological Administration of China, which applies data quality control before releasing these data.

The monthly streamflow data from three hydrological gauging stations (Linjiacun: LJC, Xianyang: XY, Huaxian: HX) were used in this study (Fig. 1). It was obtained from the Institute of Soil and Water Conservation of the Chinese Academy of Sciences and Ministry of Water Resources (http://loess.geodata.cn/), covering the period 1960 to 2012. The spatial variations are represented by these three hydrological stations from upstream to downstream, which have significant differences of catchment areas: 30 661 km2 for Linjiacun at upstream, 46827 km2 for Xianyang at middle-reach, and 106498 km2 for Huaxian at downstream.

Methodology

Meteorological drought index

The SPI developed by McKee et al. (1993) was used in this study because of its popularity and easiness to use, as well as its effectiveness and suitability in this case study. Nalbantis and Tsakiris 2009 documented the meteorological drought at multiple time scales by using SPI with hydrological years. In the Weihe River Basin, a hydrological year is generally from March to the next February, thus the four time scales, i.e., March–May, March–August, March–November, and March–February (one complete hydrological year), were used in this study.

Based on monthly precipitation, Nalbantis and Tsakiris (2009) presented the equation to calculate the cumulative precipitation depth Ri, k:

$$ {R}_{i,k}=\sum \limits_{j=1}^{3k}{P}_{i,j}\kern3em i=1,2,\dots, n\kern3em j=1,2,\dots, 12\kern3em k=1,2,3,4 $$
(1)

where Pi, jis the monthly precipitation, idenotes the hydrological year, j is the month within that hydrological year, and the k is the time scale, in which k = 1 is for March–May, and k = 4 is for March–February.

There are two equations, i.e., Eq. (2) and Eq. (3), to calculate SPI depending on precipitation distribution (Nalbantis and Tsakiris (2009): Eq. (2) was applied to the standardized precipitation volume, and Eq. (3) was applied to precipitation with a skewed probability distribution.

$$ SP{I}_{i,k}=\frac{R_{i,k}-{\overline{R}}_k}{S_k}\kern3em i=1,2,\dots, n\kern3em k=1,2,3,4 $$
(2)

where \( \overline {R_k} \) and Sk are the mean and the standard deviation of the cumulative precipitation depths, respectively.

$$ {\mathrm{SPI}}_{i,k}=\frac{w_{i,k}-\overline {w_k}}{s_k},\kern0.4em i=1,2,...,n;\kern0.6em k=1,2,3,4 $$
(3)

where

$$ {w}_{i,k}=\ln \left({R}_{i,k}\right),i=1,2,...,n;k=1,2,3,4 $$
(4)

was the natural logarithms of cumulative precipitation and \( \overline {w_k} \) and Sk are the mean and the standard deviation of these logarithms, respectively.

The classification of meteorological droughts based on Nalbantis and Tsakiris (2009) was also used in this study: non-drought (SPI ≥ − 0.5), mild drought (− 1.0 ≤ SPI < − 0.5), moderate drought (− 1.5 ≤ SPI < − 1.0), severe drought (− 2.0 ≤ SPI < − 1.5), extreme drought (SPI < − 2.0).

Time series of long-term records (1960–2012) of monthly precipitation at each station was used as input to calculate SPI. Skewness coefficients of areal precipitation for all periods were calculated on original data series, as shown in Table 1.

Table 1 Skewness coefficient of areal precipitation and their natural logarithms
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Different lengths of time scale to compute drought indices were used to explore the different drought characteristics. For example, SPI-3 only uses the sum of precipitation from March to May, which is normally the dry season in the study basin. This spring drought is critical for regional winter-wheat growth. However, the trends of drought severity and drought duration, as well as relationship between meteorological and hydrological droughts, are then investigated with the same time scale, i.e., SPI-12.

Hydrological drought index

Based on the SPI concepts, Nalbantis (2008) proposed the SDI which characterized hydrological droughts:

$$ {V}_{i,k}=\sum \limits_{j=1}^{3k}{Q}_{i,j},i=1,2,...,n;j=1,2,...,12;k=1,2,3,4 $$
(5)
$$ {\mathrm{SDI}}_{i,k}=\frac{V_{i,k}-\overline {V_k}}{s_k},\kern0.36em i=1,2,...,n;k=1,2,3,4 $$
(6)

or

$$ {\mathrm{SDI}}_{i,k}=\frac{y_{i,k}-\overline {y_k}}{s_k},\kern0.6em i=1,2,....,n;\kern0.5em k=1,2,3,4 $$
(7)
$$ {y}_{i,k}=\ln \left({V}_{i,k}\right),i=1,2,...,n;k=1,2,3,4 $$
(8)

where Vi, k is the cumulative streamflow volume for the ith hydrological year and the kth reference period; \( {\overline{V}}_k \) and sk are the mean and the standard deviation of cumulative streamflow volumes of reference period k,  respectively. The yi,k is the log transformation of streamflow volume.

The skewness coefficients of the raw streamflow, its natural logarithms, and the final choice dataset are shown in Table 2. All three stations showed a skewed distribution, so a natural logarithm transformation was needed to estimate SDI with Eq. (7).

Table 2 Skewness coefficient of streamflow, and their natural logarithms
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Results and discussion

Meteorological droughts

The meteorological drought index SPI, based on four time scales, are shown in Fig. 2 for three stations. It is clear that the frequency of drought events has an increasing trend, especially after 2005 when SPIs were always negative. These results agreed with the results previously reported by Liu et al. (2014). In addition, the drought events were not the same from different computing time scales: The significant discrepancies were observed only when compared between the 3-month time scale (March–May) and the 6-month time scale (March–August), and between the 6-month time scale (March–August) and the 9-month time scale (March–November). Decent agreements were obtained between the 9-month time scale (March–November) and the hydrological year (March–February). Considering the 3-month time scale and the 12-month time scale, severe drought event (−2.0 ≤ SPI <  − 1.5) occurred more frequently around each station in the case of the 3-month time scale than the 12-month time scale. In addition, the fluctuation range of the 3-month time scale was bigger than those of other time scales, and the range of the 12-month time scale was the smallest. The synthesis result indicated that the drought event state varied with the increasing of SPI time scales, generally a decline trend. It is because that computation of the SPI in the 12-month time scale aggregated total precipitation from March to February, which included both dry and wet seasons. However, SPI-3 was only accounted for the sum of precipitation from March to May, which is normally dry season in the study basin.

Fig. 2
figure 2

Temporal variation of meteorological drought. (A) Linjiacun, (B) Xianyang, and (C) Huaxian stations

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Figure 3 shows the meteorological drought severity of three stations during 1960–2012 based on the 12-month time scale. The years of the entire basin which were struck by drought (SPI < 0) are as follows: 1969, 1971, 1972, 1977, 1979, 1982, 1986, 1987, 1991, 1994, 1995, 1997, 1999–2002, 2004, 2006, 2008, and 2009. That is consistent with the severe drought years of Weihe River Basin based on “Chinese historical droughts records (1949–2000)” (Huang et al. 2015a, 2015b). It is found that year 1997 was the driest year and it has severe drought for Xianyang and Huaxian stations used in this study. In addition, all three stations experienced moderate drought in years 1986 and 2008; in other years (except 1969, 1997, 1982, 1986, 1991, 1995, 1997, 2008, and 2009), it is found only mild drought in three stations. It is also found that the meteorological drought severity was increasing in the past 52 years; the severity of meteorological droughts has the most significant trend in the downstream at Huaxian station.

Fig. 3
figure 3

Meteorological drought severity at three stations during 1960–2012 based on 12-month SPI

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The Mann-Kendall method (Fu et al. 2004) was used to analyze the tendency of the meteorological drought numbers of months within a year at three stations, based on the 12-month time scale (Fig. 4). Overall, it showed an increasing trend during 1960–2012 for all three stations. However, spatial differences can be observed from upstream to downstream: The Mann-Kendall statistic Z-value was 2.25 at upstream Linjiacun station, and 1.93 at middle-reach at Xianyang station, but reduced to 0.70 (statistically insignificant) at downstream Huaxian station.

Fig. 4
figure 4

Meteorological drought number of months at three stations during 1960–2012 based on 12-month SPI

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Hydrological droughts

The SDI series for different time scales are shown in Fig. 5. It indicated that the hydrological drought occurrences had an obvious trend of increasing over the last five decades. As shown, the majority of the droughts in three stations were found from 1977 to 1980, 1996, 1998, and 2001–2003. These results confirmed the results obtained by Bai et al. (2012). There were more drought events in the case of the 3-month time scale than in the 12-month time scale. This reason is that, in the study region, much of the precipitation in the winter falls as snow, and accordingly the spring snowmelt may change the river flow regimes with increase of the river flows in the March–May season.

Fig. 5
figure 5

SDI series for different reference periods during 1960–2012. (A) Linjiacun, (B) Xianyang, and (C) Huaxian stations

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Figure 6 shows the hydrological drought severity of three stations during 1960–2012, based on the 12-month time scale. It was found that the hydrological drought severity was increasing in Weihe River basin. Figure 7 presents the numbers of month with hydrological drought events in a year. As a whole, it is clear that frequency (e.g., the numbers of months with a drought event) of hydrological droughts was increasing during 1960–2012 in the Weihe River basin. The upstream Linjiacun station showed the most statistically significant trend with a Z-value of 4.47 (p < 0.0000). In contrast, the trend was statistically insignificant at downstream Huaxian station, although it still showed an increasing trend.

Fig. 6
figure 6

Hydrological drought severity at three stations during 1960–2012 based on 12-month SDI

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Fig. 7
figure 7

Hydrological drought number of months at three stations during 1960–2012 based on 12-month SDI

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Relationship between meteorological and hydrological droughts

Establish regression function between SPI and SDI

From the regression coefficient (slope) and the determination coefficient (R2) of the linear regression equations (Table 3), it can be found that the correlations between SPI and SDI become stronger with the time scale increasing. The determination coefficients of the 9-month time scale and the 12-month time scale were higher than those of the other two time scales. For example, it was 0.772 at the Huaxian station for the 9-month time scale. In addition, the correlation between SPI and SDI generally became stronger from upstream to downstream. For example, the determination coefficients at the 9-month time scale were 0.579, 0.636, and 0.772 at the Linjiacun station (upper stream), the Xianyang station (middle reach), and the Huaxian station (downstream), respectively.

Table 3 Regression coefficient (a) and determination coefficient (R2) of linear regression equations of SDI on SPI
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Figure 8 shows the regression lines and the associated data points, which could be used to forecast the hydrological droughts based on the meteorological droughts. The linear regression models for the 9-month time scale were the best at all three stations.

Fig. 8
figure 8

Linear regression of SDI on SPI for each time scale ((a) for period March–May as 3-month time scale, (b) for period March–August as 6-month time scale, (c) for period March–November as 9-month time scale, (d) for period March–February as 12-month time scale)

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Identification of lag time between the drought indices

To better identify the correlation between SPI and SDI, a moving average was carried out for multiple time scales (Fig. 9). Results indicated that the variations of SPI and SDI were similar during 1960–2012, and the differences between them do exist. For example, the correlation was weak at Linjiacun station after 1995. Generally speaking, the relationship between SPI and SDI was the strongest at downstream Huaxian station. This can be explained with the construction of storage reservoirs affecting the hydrological characteristics.

Fig. 9
figure 9

The moving average of SPI and SDI at the study stations for different time scales ((a) for period March–May as 3-month time scale, (b) for period March–August as 6-month time scale, (c) for period March–November as 9-month time scale, (d) for period March–February as 12-month time scale)

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With the time scale increasing, the correlation between meteorological and hydrological droughts became stronger at every station (Fig. 10). As a whole, the SPI was exceeding 1 month than SDI for the 3-month scale and for the 12-month scale at every station. The correlation coefficient was 0.892 at Huaxian station. For the 6-month and 9-month time scales, SDI was 2 months lagging than SPI. This timeframe of lagging time was consistent with a previous study (Tabrizi et al. 2010).

Fig. 10
figure 10

The correlation coefficient about lead-lag between SPI and SDI at the study stations for the years 1960–2012

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The differences between SPI and SDI

The differences between SPI and SDI have increased during the last 50 years. The main reason was due to the decreases of precipitation and runoff, which is caused by natural climate change and variability, as well as human activities (He et al. 2015). Climate change and variability included, but is not limited to, the variation of precipitation, temperature, and potential evapotranspiration (Fu et al. 2007a), and human activity has many different aspects, such as, increased water diversion, expanded irrigation area strengthened, changed land use/cover, and soil and water conservation (Fu et al. 2004).

The precipitation had a decreasing trend during the years 1960–2012 (Fig. 11). For example, the average annual precipitation decreased from 556.86 mm during 1960–1986 to 495.8 mm during 2001–2012. The decreased magnitudes of precipitation were larger in Linjiacun station, the upper stream of the Weihe River Basin, than that in Huaxian station, the lower reach. The result was generally consistent with that from Shen and Qiang (2014), who found that the annual precipitation in the Weihe River Basin had an overall decline trend with a clear spatial patterns. Simultaneously, the runoff coefficient also had a decline trend at all three stations (Fig. 12). For example, the mean runoff coefficient was 0.147 during 1960–1986, but 0.096 during 2001–2012 in Linjiacun station. Bi et al. (2013) found that the primary driving factor for the runoff decrease was precipitation change in the Weihe River Basin.

Fig. 11
figure 11

Annual precipitation changing trend during the years 1960–2012

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Fig. 12
figure 12

The runoff coefficient during the years 1960–2012

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In addition, streamflow was sensitive to both precipitation and temperature. Fu et al. (2004) analyzed the monthly temperature in the Yellow River watershed increased about 1 °C during the years 1951–1998 for January, February, and December. The increasing temperature would lead to an increasing PET change. Bi et al. (2013) pointed that the PET increased 35.0 mm caused by the raising temperature in the Weihe River Basin during the years 1995–2009. Fu et al. (2007a, 2007b) also have demonstrated the precipitation and temperature elasticity of streamflow, and pointed that 20% precipitation increase may result in a streamflow increase of 48% if the temperature is 1 °C lower but only a 4% increase if the temperature is 1.8 °C higher than the long term. Yu et al. (2010) have built a non-linear relationship between streamflow and both precipitation and temperature and found that streamflow has greater sensitivity to precipitation than to temperature. Huang et al. (2015a, 2015b) found that climate changes were the major driving factors on the runoff decrease in the 1970s, 1990s, and 2000s, whose contributions were 54.25%, 60.35%, and 57.39%, respectively.

The annual runoff depth also had an obviously declining trend during 1960–2012 (Fig. 13). For example, the mean annual runoff was 84.66 mm during 1960–1986, while that was 48.97 mm during 2001–2012. This was similar to those from Guo et al. (2016), who indicated that in addition to precipitation, there are some other non-precipitation factors that are responsible for the change about runoff, such as human activities. Human activities affect in many ways, and the following specific human activities were particularly related to the decrease of runoff in the Weihe River Basin.

  1. 1)

    High-speed economic development and the increasing population have been the driving force for the increase of the industrial and living water demand and water use. The average population density was 1300–1400 people per square kilometer in 2005, and the growth of economy and the increase of consumption aggravated water demand (Zhang et al., 2010).

  2. 2)

    The irrigation areas have expanded over the last five decades. There were 2 reservoirs in the Weihe River Basin in 2000 with the total reservoir storage of 2.73 billion m3 and utilizable capacity of 1.55 billion m3. The effective irrigation area was about 121,000 hm2 (Bi et al. 2013). There were seven large irrigation areas: Jing-hui-qu (completed in 1935), Yang-mao-wan (completed in 1970), Jiao-kou (completed in 1970), Bao-ji-xia (completed in 1971), Tao-qu-po (completed in 1980), Feng-jia-shan (completed in 1982), Shi-tou-he (completed in 1990). Among these, the Bao-ji-xia irrigation area was the largest, and its annual average water diversion was 580,000 m3 (Chang et al. 2015). The main use of water in terms of human activities was agricultural irrigation in the study basin, and the irrigation area expansions have resulted in the decrease of observed runoff (Fu et al. 2004).

  3. 3)

    The changing of land use has increased water demand, which aggravated hydrological drought. Land use is a major way by which humans change the natural environment and is a main driving force of land cover change (Fu et al. 2004). Land use change can directly affect the surface runoff and watershed runoff yield. He et al. (2015) found that the area covered by forest increased from 358.4 thousand hectares in 1980 to 383.0 thousand hectares in 2005. The grassland area decreased from 2030.1 thousand hectares in 1980 to 1958.0 thousand hectares in 1985 and then increased from 1965.2 thousand hectares in 1996 to 2035.7 thousand hectares in 2005. The arable land declined intermittently from 1891.1 thousand hectares in 1980 to 1851.5 thousand hectares in 2005 in Jinghe River, which is the second-longest tributary of the Weihe River Basin. Chang et al. (2015) pointed out that large-scale soil conservation practices, such as afforestation and grass-planting creation of level terraces, played an important role in the regulation of runoff and water conservation in the Weihe River Basin.

  4. 4)

    Other factors exist for the differences about meteorological and hydrological droughts besides the three major reasons, such as groundwater exploitation, snowmelt, urbanization, mining industry, and climate extremes.

Fig. 13
figure 13

Annual runoff depth during the years 1960–2012

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Conclusions

The frequencies of meteorological and hydrological droughts have shown an increasing trend during the last 50 years in the Weihe River Basin. Meteorological moderate drought events and hydrological drought events occurred more frequently in the upper and middle reaches of the Weihe River Basin based on the 12-month time scale.

The regression coefficients of a linear regression between SPI and SDI indicated that with the time scale increasing, the regression coefficients became stronger.

The reason for the differences between meteorological and hydrological droughts included, but were not limited to, climate change and variability, human activities, and land use/cover changes.

This study investigated the relationships between the meteorological and hydrological drought events with SPI and SDI, and a simple linear function between them was built. The occurrence of hydrological drought events usually lagged meteorological droughts for 1–3 months depending on the calculated time scale and stations. The differences between meteorological drought and hydrological drought became larger due to climate change and human activities. One of our next step studies will explore the impacts of climate change on hydrological drought at basin scale (Zhao et al. 2019). This relationship between meteorological and hydrological droughts presented in this study can be used for the long-term forecasting of droughts and early warning water resources management in practice.