1 Introduction

Drought is a natural hazard that results from a deficiency of precipitation from expected or “normal” which is insufficient to meet the demands of human activities and the environment. This precipitation deficit may build up quickly over a period of time, or it may take months before the deficiency begins to appear in reduced stream flows, reservoir levels or increased depth to the underground water table (Badripour 2007). Although there is not a universal definition of drought, in the most general sense, drought can be defined with different disciplinary perspectives, namely, meteorological drought, agricultural drought, hydrological drought and socioeconomic drought (Yang 2010). The first three groups could be defined as physical phenomenon. The last group deals with drought in terms of supply and demand, tracking the effects of water shortfall as it ripples through socioeconomic systems (Wilhite and Glantz 1985). Among the different types of droughts, the hydrological component is the most important given the high dependence of many activities (industrial, urban water supply and hydropower generation) on surface water resources (Vasiliades et al. 2011). Hydrological drought initially caused by rainfall deficits, is normally associated with reservoirs or lake levels within a basin (Liu et al. 2012). In fact, hydrological droughts can have widespread impacts by reducing or eliminating water supplies, deteriorating water quality, restricting water for irrigation and causing crop failure, reducing power generation, disturbing riparian habitats, limiting recreation activities, and affecting a diversity of economic and social activities (Mishra and Singh 2010).

The simplest way for monitoring drought conditions is to use drought indices, because they provide a quantitative method for determining the onset and end of a drought event, because the index value indicates the level of drought severity. Several drought indices were developed to characterize hydrological droughts over the years (Dracup et al. 1980; Tate and Gustard 2000; Smakhtin 2001; Heim 2002; Tallaksen and van Lanen 2004). Yevjevich (1967) used the statistical theory of runs to analyze drought events. The Surface Water Supply Index (SWSI) designed by Shafer and Dezman (1982), incorporated snowpack, streamflow, precipitation, and reservoir storage to complement the Palmer Index for moisture conditions across Colorado. It was developed for mountainous regions where spring snowmelt contributes significantly to surface water reserves. The regional deficiency index (RDI), developed by Stahl (2001), uses daily flow data and removes the influence of streamflow seasonality on droughts. The index does not indicate the magnitude of a drought–it only quantifies the duration from a binary time series–and it quantifies drought severity by the surface affected. This makes comparisons of hydrological droughts at different stations impossible (Vicente-Serrano et al. 2012). Keyantash and Dracup (2004) developed an aggregate drought index (ADI) evaluated within three diverse climate divisions in California. The ADI comprehensively considers all physical forms of drought (meteorological, hydrological, and agricultural) through selection of variables that are related to each drought type. This index is not yet used operationally due to high data requirements and complexity.

Pandey et al. (2008) defined the drought severity index (DSIe) as a function of (1) the ratio of deficit flow volume to corresponding volume at the truncation level and (2) the ratio of duration of deficit flow to the maximum possible duration of the independent streamflow drought event. Shukla and Wood (2008) developed the standardized runoff index (SRI) based on the standardized precipitation index (SPI) developing concepts to analyze simulated runoff data on different time scales. They applied the physically based, semi-distributed macro-scale variable infiltration capacity (VIC) model outputs for estimating runoff and subsequently the SRI. In this index, the hydrological drought index is derived by transforming monthly streamflows into z-scores. Fleig et al. (2010, 2011) explored the links between severe hydrological droughts and weather types and proposed a new index-Regional Drought Area Index (RDAI), based on daily streamflow, to represent the drought affected area in north-western Europe. Sharma and Panu (2010) suggested the use of a standardized hydrological index (SHI) as a measure for defining and modeling hydrological droughts. The concept of SHI is analogous to SPI (Mckee et al. 1993), as used in the context of meteorological droughts, except that SPI represents a standardized and normalized entity, whereas SHI is only a standardized entity and thus implicitly inherits the non-normal character of the flow series (Sharma and Panu 2012). Araghinejad (2011) proposed an approach to monitor and forecast hydrological drought in a probabilistic manner. The proposed approach deals with the supply and demand variables and the role of carryover in a system to estimate the probability of drought severity at different hydroclimatlogical conditions as well as different storage volume levels.

The indices devised for characterizing hydrological drought, in general, are data demanding and computationally intensive. In contrast, the streamflow drought index (SDI), developed recently by Nalbantis and Tsakiris (2009), is a very simple and effective index for hydrological droughts. Considering limited available research on hydrological drought monitoring by the SDI, this study was conducted in the context of an on-going project to assess hydrological drought by this index in the northwest of Iran. The SDI was used for overlapping periods of 3, 6, 9 and 12 months within each hydrological year over the period 1975–2009.

2 Study Area and Data

The province of West Azerbaijan with an area of 39,487 km2 is located on the northwest of Iran. The province has a mountainous terrain in which the high Zagros Mountains span over an area from the northwest to the southeast. The water obtained from the melting snow flows through the various valleys in the vicinity, ultimately flowing into the Lake Urmia and the Kloy (Zaab) River. Climatically, the province is largely influenced by the rainy winds of the Atlantic Ocean and Mediterranean. Cold northern winds affect the province during winter and cause heavy snow. Generally the climate is variable, with temperature rising to 34 °C in July and dropping to −16 °C in January. Average annual precipitation ranges from 870 mm of rainfall equivalent in exposed southern areas down to around 300 mm in the north of which a substantial proportion is snow.

The monthly observed streamflow data were collected from 14 hydrometric stations. Data cover the period from 1975–1976 to 2008–2009. The elevation of the stations ranges between 1200 and 1650 m. Station maintenance and data archiving are under the supervision of the West Azerbaijan Regional Water Co. Hydrometric stations position used in this study is shown in Fig. 1 and their geographical coordinates are presented in Table 1.

Fig. 1
figure 1

Geographic location of the study area and spatial distribution of the hydrometric stations

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Table 1 Details of the hydrometric stations used in the study
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3 Methods

3.1 The Streamflow Drought Index (SDI)

Based on the SPI developing concepts, the SDI was developed by Nalbantis and Tsakiris (2009) for characterizing hydrological drought. Hydrological year is from October to the September of every next year in Iran, and so four overlapping time periods (hereafter as reference periods) are utilized within each hydrological year: October–December, October–March, October–June, and October–September (one complete hydrological year).

To compute SDI, it is assumed that a time series of monthly streamflow volumes Q i, j is available where i denotes the hydrological year and j the month within that hydrological year (j = 1 for October and j = 12 for September). Based on this series, cumulative streamflow volume is computed as follows:

$$ {V_{i,k}} = \sum\limits_{j = 1}^{3k} {{Q_{i,j}}} {\rm{ }}i = 1,2, \ldots {\rm{ }}j = 1,2, \ldots ,12{\rm{ }}k = 1,2,3,4 $$
(1)

where V i,k is the cumulative streamflow volume for the i-th hydrological year and the k-th reference period, k = 1 for October–December, k = 2 for October–March, k = 3 for October–June, and k = 4 for October–September.

The SDI is defined based on cumulative streamflow volumes V i,k for each reference period k of the i-th hydrological year as follows:

$$ SD{I_{i,k}} = \frac{{{V_{i,k}} - \overline V }}{{{s_k}}}{\rm{ }}i = 1,2, \ldots {\rm{ }}k = 1,2,3,4 $$
(2)

where Vk and sk are respectively the mean and the standard deviation of cumulative streamflow volumes of reference period k as these are estimated over a long period of time. In this definition the truncation level is set to Vk although other values could be used (Nalbantis 2008; Nalbantis and Tsakiris 2009).

Positive SDI values reflect wet conditions while negative values indicate a hydrological drought. Based on the SDI, five states of hydrological drought are defined which are denoted by an integer number ranging from 0 (non-drought) to 4 (extreme drought). The states of hydrological drought are defined through the criteria of Table 2.

Table 2 Definition of states of hydrological drought based on SDI (Nalbantis and Tsakiris 2009)
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4 Results and discussion

The hydrological drought index of Eq. 2 is identical to the standardized streamflow volume. It is expected that streamflow values do not follow the normal distribution and possess a skewed probability distribution. The Kolmogorov- Smirnov (K-S) test at the 0.10 significance level was used to check the goodness of fit of the streamflow data to the normal distribution (Table 3). It should be noted that the null hypothesis of K-S test is that the observed data is come from the proposed distribution, and hence, higher p-values are interpreted as tendency toward accepting the null hypothesis. As the results show, the 9-month (October–June) and 12-month (Year) streamflows with the p-values greater than 0.13 had a normal distribution. For the October–December (3-month) and Oct–March (6-month) series, the normal distribution provided an adequate fit to the streamflow series because the p-values were in most cases higher than the critical value of 0.10. Only the October-March streamflow series at three stations (Tapik on Nazloo-Chai river, Hashem-Abad on Barandooz-Chai river and Marz Sero station on Berdook river) did not follow the normal distribution. Furthermore, the October–December streamflow series at three stations (Abajaloo station on Nazloo-Chai river, Band-e-Urmia station on Rozeh-Chai river and Ourban station on Dirali-Chai river) did not follow the normal distribution. In addition, the p-value of the October–December streamflow series at Hashem-Abad station of the Barandooz-Chai river is close to being significant at the 0.10 significance level.

Table 3 The p-value of the Kolmogorov–Smirnov test for streamflow volume data
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It is interesting that the maximum skewness of the October–December streamflow values was found at Abajaloo station located along with the Nazloo-Chai river, while the minimum skewness was obtained at Chahrigh station on this river. Vicente-Serrano et al. (2012) also showed that there is no clear spatial pattern in the probability distributions and the probability distribution providing the best fit for gauging stations along the same river course often changed.

We used the log-normal, exponential and uniform distributions for decreasing the skewness from the streamflow series for all the reference periods. Table 4 presents the percentage of the streamflow volume series in which each probability distribution shows the best fit (highest p-value). For the 3-month period (October–December), the log-normal distribution showed the best fit for 50 % of the series; the exponential distribution showed the best fit for 29 % of the series; and the uniform distribution showed the best fit for 21 % of the series. For the 6-month period (October–March), the log-normal, exponential and uniform distributions showed the best fit for 79 %, 14 % and 7 % of the series, respectively. Moreover, the log-normal distribution was the most suitable probability distribution to fit the streamflow series of the 6-month and yearly periods, which showed the best fit for 100 % of the series. In general, the log-normal and uniform distributions were respectively the most and least suitable probability distributions to fit the streamflow series at the study area.

Table 4 Percentage of the streamflow volume series in which each probability distribution shows the best fit
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Figure 2 shows representative example of the evolution of the streamflow volume series at Ourban station with different probability distributions. The p-values for fitting normal and uniform distributions to the October–December streamflow series at the Ourban station are less than 0.05, while the p-value of fitting log-normal and exponential distributions is very high (greater than 0.47). For the other streamflow series at the station, the log-normal distribution seems to be the best choice.

Fig. 2
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Results of the Kolmogorov–Smirnov test to fit distributions for different time-scales of accumulated streamflow

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Several studies have recommended using the log-normal distribution to fit streamflow data (Kroll and Vogel 2002; Zaidman et al. 2002; Yue and Wang 2004; Chen et al. 2006; McMahon et al. 2007; Nalbantis 2008; Shukla and Wood 2008; Nalbantis and Tsakiris 2009; Yang 2010). Vicente-Serrano et al. (2012) pointed out that using this distribution is inappropriate in a region with high variability in the river regimes and streamflow characteristics. Hence, due to the best performance and simplicity of the log-normal distribution, it was used to fit the streamflow series for calculating an SDI. After logarithmic transformation of the dataset, the SDI was computed as the cumulative streamflow anomaly of the transformed data, divided by the standard deviation of the transformed data.

The SDI series for the reference periods October–December and October–March are shown in Figs. 3 and 4 respectively, based on the 33-year time series data. As shown, the majority of the extreme droughts for the reference periods October–December and October–March were found in the last 12 years from 1997–1998 to 2008–2009. All of the stations experienced at least one extreme drought except Abajaloo and Hashem-Abad stations for the reference period October–December and Tapik and Hashem-Abad stations for the reference period October–March.

Fig. 3
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SDI series at the study stations for reference period October–December

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Fig. 4
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SDI series at the study stations for reference period October–March

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The SDI series for the reference periods October–June and the hydrological year (October–September) are depicted in Figs. 5 and 6, respectively. All of the rivers of the study region exception for the Derik-Chai river (Nazar-Abad station) faced at least one extreme drought during the last decades. The most sever drought can be identified at Hashem-Abad station located along with the Barandooz-Chai river in 2000–2001 with SDI value equal to −3.15. Furthermore, all of the extreme drought events occurred in the last 11 years from 1998–1999 to 2008–2009. In general, the hydrological years of 1998–1999, 1999–2000 and 2000–2001 were the driest years. In other words, the most sever streamflow drought occurred during the hydrological year of 1998–1999, 1999–2000 and 2000–2001. The most sever streamflow drought for Band-e-Urmia station located along with the Rozeh-Chai river occurred during year 2000–2001, with a yearly (October-September) SDI value of −2.51. At another station located along with the Rozeh-Chai river (i.e., Kalhoor), the most sever streamflow drought occurred just 1 year earlier, during 1999–2000, with the October-September SDI value of −2.26. Nikbakht et al. (2012) characterized streamflow drought by the percent of normal index (PNI) in Northwest Iran. They found the most sever streamflow droughts in 1999–2000 and 2000–2001. Over half the Iran’s population has been affected by prolonged droughts in 1998–2001 period (Raziei et al. 2009). The 1999 drought was most devastating to agriculture and water resources of the country, causing massive movement of people from rural to urban areas (Yazdani and Haghsheno 2008). In addition, about twenty provinces in the country have experienced precipitation shortfalls during 2001 (Agrawala et al. 2001). The United Nations estimates the damages to agriculture and livestock at $2.5 billion in 2001, up from $1.7 billion in 2000. After 3 years of extreme drought during 1998–2001, which the United Nations has said is the most severe in Iran for 30 years, most of the country's wetlands have dried out and many farmers are struggling to survive.

Fig. 5
figure 5

SDI series at the study stations for reference period October–June

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Fig. 6
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SDI series at the study stations for reference period October–September

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The river flows of the study region have a dominant role in the water balance of the Lake Urmia as one of the largest permanent hypersaline lakes in the world. In a recent drought of the Urmia basin, which started in 1999, the water level of the Lake Urmia dropped from 1277.80 m to 1273.35 m (Heidari et al. 2010). Drought conditions, together with the increasing needs for agricultural and potable water, have reduced significantly the volume of water entering the lake so that, at present, the Lake Urmia has shrunk significantly and large areas of the former lake bed have been exposed (Eimanifar and Mohebbi 2007).

In addition, the persisting and intensifying hydrological droughts causing the scarcity of water and depleted supplies for irrigation will adversely affect agricultural production in the region, particularly for those farmers located at the downstream of the rivers. In 2001, farmers are expecting 35-75 % reductions in wheat and barley production in the drought affected provinces.

The results also indicated that several drought events lasted more than 1 year in the study area. For example, the sever drought year 1998–1999 at Miandoab station lasted for 4 years. Meanwhile, the study region faced wet conditions during the period from 1984–1985 to 1996–1997. According to the yearly (October-September) streamflows, the hydrological year of 1992–1993 was the wettest year in the Nazloo-Chai river (i.e., Abajaloo, Chahrigh and Tapik stations). The Barandooz-Chai river (i.e., Babarood, Dizaj and Hashem-Abad stations) experienced the wettest period during 1997–1998. Similarly, the wettest period in the other rivers occurred in 1992–1993 (for six stations) and 1997–1998 (for two stations).

The areal SDI series for different reference periods are illustrated in Fig. 7. Significant differences were observed when passing from the first 3-month period (October–December) to the first semester (October–March) and also passing from the 6-month period (October–March) to the 9-month period (October–June). Nalbantis and Tsakiris (2009) found that there are significant discrepancies only when passing from the first 3-month period (October–December) to the first semester (October–March). They stated that the discrepancy is due to the typical Mediterranean hydrological regime which is manifested as a wet period of 6 months of the hydrological year and a mostly dry period thereafter. In the study region, much of the precipitation falls as snow in the higher elevations and spring snowmelt may change the river flow regimes with increasing the river flows.

Fig. 7
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Areal SDI series for different reference periods

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As the results show, good agreements were obtained when passing from the 9-month period (October–June) to the hydrological year (October–September). According to the results (Fig. 7), the most sever streamflow drought occurred during the hydrological year of 2000–2001, with the average SDI values about −2 for the 9 and 12 months periods.

5 Conclusions

This study estimated hydrological droughts by using the streamflow drought index in the mountainous regions of northwestern Iran over the period 1975–2009. The capability of the log-normal, exponential and uniform probability distributions was tested in order to select the most suitable distribution to fit the streamflow data. The results of the goodness-of-fit K-S test showed that the log-normal distribution was the best fit probability distribution for the streamflow series. Furthermore, the hydrological drought analysis based on the SDI for 3, 6, 9 and 12 months periods indicated that almost all the stations experienced extreme droughts during the study period. The extreme drought events occurred mainly in the last 12 years from 1997–1998 to 2008–2009 and the hydrological years of 1998–1999, 1999–2000 and 2000–2001 were the driest years during the examined period.