Introduction

Drought is a long-term meteorological hazard that causes adverse impacts on water, agriculture, society, economy, and ecosystems (Singh et al. 2014; Huang et al. 2019). It is one of the deadliest natural hazards. For example, from 1900 to 2016 due to major droughts worldwide, 1.582 billion people were affected and 11.4 million died (Statista 2016). Droughts increase water stress by 80% in some regions (Stewart et al. 2020). They reduce societal and economic adaptive capacity (Desbureaux and Rodella 2019). Sustained droughts cause hydrological changes in soil moisture (Sehgal and Sridhar 2019), surface water (Mishra 2020), and groundwater resources (Jang et al. 2020) and long-term water storage (Moon et al. 2018). Evaluation of the impact of future droughts due to climate change on the gross domestic product (GDP) shows that socio-economic vulnerability may increase by up to 70% in some regions (Liu and Chen 2021).

The variability of drought characteristics is critical in arid and semi-arid climates as it causes immediate water stress (Schwabe et al. 2013). The changing pattern of drought severity (DS) as an environmental hazard with far-reaching implications has been analyzed in other works (Yao et al. 2018; Trabelsi et al. 2019). The results of these studies confirm an increasing trend of DS in Ethiopia (Kassaye et al. 2020). Concerns about the potential impact of climate change on DS have led to a rich body of research (e.g., Blenkinsop and Fowler 2007; Wang et al. 2018). Increasing drought intensity in recent decades has been confirmed in some regions in the world (Azam et al. 2018; Byakatonda et al. 2018). Drought characteristics will continue to change due to climate change (Wang et al. 2018), and increased DS has been projected (Loukas et al. 2008; Wang et al. 2018). Wang et al. (2018) found that the projected increasing potential evapotranspiration (PET) will cause higher drought severity.

Linking drought characteristics and atmospheric teleconnection patterns is one of the methods to assess climate variability–related drought conditions, exploiting this long-term spatial memory (Gao et al. 2019). In different parts of the world, connections between these teleconnection fluctuations and the variability of rainfall and drought have been found (Zambrano Mera et al. 2018; Ndehedehe et al. 2020).

There are various methods to study drought characteristics such as wavelet transform (Sharma and Goyal 2020; Li et al. 2020), copula modeling (Yang et al. 2020; Kiafar et al. 2020), and logistic regression (Ford and Labosier 2014). Many studies have focused on drought persistence throughout the world (Ault et al. 2014; Munshi 2015a, b; Tatli 2015; Moon et al. 2018; Tong et al. 2018). Persistence indices are used to understand the memory within time series, and the Hurst exponent is one of the most useful indices. The Hurst exponent is a useful tool to detect non-linear phenomenon in natural processes (Wang et al. 2011) and to facilitate calculation of drought persistence (Tatli 2015; Dey and Mujumdar 2018).

The Hurst exponent has been used in some environmental sciences such as hydrology (Hurst 1951) and geomorphology (Luo et al. 2019). Using the Hurst exponent in climatological studies, Munshi (2015) detected persistence and long-term memory in temperature and precipitation time series in the tropical Andes (Poveda 2011). Chandrasekaran et al. (2019) showed the appropriate performance of this index in assessing the similarity of rainfall time series. Tatli (2015) by using the Hurst exponent found that drought persistence could be derived from DS in Turkey. Exploration of drought characteristics using the Hurst exponent in Iran has not yet been studied.

High-frequency drought events are persistent risks and one of the climatic characteristics of Iran (Doostan 2016). In recent years, concerns have been raised about increasing droughts and aridity in Iran. Hadi Pour et al. (2020) found that 4.84% of semi-arid regions have decreased due to increasing droughts replaced by arid ones. Since Iran is an arid and semi-arid country, the changing characteristics of DS affect the process of aridity (Tabari et al. 2014) and desertification (Akbari et al. 2020; Ghorbani et al. 2018). The trend of increasing drought intensity in Iran has been accompanied by a concurrent increase in its duration (Dargahian and Razavi Zadeh 2020). Figure 1 shows the average DS using the standardized precipitation (SPI) in Iran from 1989 to 2018. According to this data, 83% of the statistical period included near normal, 6.7% moderately wet, and 10% moderate drought based on the SPI category.

Fig. 1
figure 1

Average drought intensity based on the SPI in Iran (1989–2018)

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The spread of droughts in Iran corresponds to the pathways of cyclones and wet air mass from the Mediterranean into Iran (Doostan 2016). The Arabian and Mediterranean Seas are the main sources of moisture for Iran’s rainfall. Changes in their moisture transfer pattern are important in determining the amount of rainfall and the occurrence of droughts (Karimi and Farajzadeh 2011). According to previous studies (Omidvar et al. 2016), due to the geographical extent of Iran, different atmospheric synoptic patterns dictate the variability of precipitation and occurrences of drought. For example, the Black Sea high-pressure system controls changes in 50% of Iran’s annual rainfall (Hosseini et al. 2015).

Studies have also been conducted to explore the relationship between Iran’s droughts and teleconnection patterns. A correlation between the El Niño–Southern Oscillation (ENSO) and the variability of precipitation and droughts in Iran has been detected (Azizi 2000; Nikraftar and Sam-Khaniani 2018). In some years, a relationship between the La Niña Oscillation and sea surface temperatures in the Indian and Pacific with DS has also been found (Golian et al. 2015). The Eastern Mediterranean Oscillation (EMO) and the North Atlantic Oscillation (NAO) are associated with increases rainfall in western Iran (Basati and Yarahmadi 2017; Toulabi Nejad et al. 2018).

The primary purpose of designing statistical and mathematical indices is to describe DS in diverse climates (Byakatonda et al. 2018). The SPI has been widely used as a useful tool for monitoring droughts in Iran (Karimi et al. 2019; Nabaei et al. 2019). The environmental and socio-economic consequences of changing and persistent DS can be significant in Iran. Due to the lack of previous studies on the application of the Hurst exponent (H) in drought studies in Iran, we have investigated its application.

Material and methods

Study area

Iran is located in an arid belt, bordered by the Caspian Sea to the north and the Persian Gulf to the south. Two mountain ranges, northern Alborz and western Zagros, control the inflow of the Mediterranean and Caspian winds to the Central Plateau (Tavassoli 2016). Mountains and deserts occupy 52% of the country’s area, and some 16% of it is 2000 m above sea level. Being surrounded by seas, oceans, and deserts and the large extent of mountain ranges have created a diverse climate in Iran (Doostan 2020). Based on the De Martonne classification index, Iran’s climate is generally arid (about 65%) and semi-arid (about 20%), and only 10% is humid (Katiraie-Boroujerdy et al. 2013). Iran is divided into six main watersheds (Fig. 2), which are as follows:

  1. 1.

    The Caspian Sea watershed is south of the Caspian Sea and along with the Alborz mountain range with an area of 174,684 km2. The Caspian Sea watershed with an average annual rainfall of 429 mm is the wettest in the entire country and consists of seven sub-basins. About 70% of the watershed area is covered by mountainous areas and 30% by plains.

  2. 2.

    The Central Plateau is in the middle of Iran and covers the largest area of the country and divided into nine sub-basins. The area of this watershed is 838,944 km2. The average rainfall in this watershed is 165 mm, which decreases from north to south. The hottest deserts of Iran are located in the Central Plateau watersheds. In this watershed, the mountainous area is 45% and the plain is 55%.

  3. 3.

    The East Boundary watershed is also known as the Hamoon-Hirmand. This watershed with three sub-basins is located on the east border of Iran adjacent to Afghanistan and Pakistan. The area of this basin is 104,783 km2. The average annual rainfall of watershed is 110 mm and is characterized by an arid climate. The area is equally covered by mountainous areas and plains.

  4. 4.

    The Karakum is situated in northeastern Iran, and the area of this watershed is 44,165 km2, of which about 67.4% is mountainous areas and 32.6% is foothills and plains. The Karakum watershed climate is semi-arid and cold in the mountainous areas and arid in the plain regions. The average annual rainfall of the watershed is 222 mm.

  5. 5.

    The Lake Urmia is in northwestern Iran, and the area of this watershed is 51,801 km2, of which about 64.6% is mountainous areas and 21.1% is foothills and plains and 14.3% is Lake Urmia. The Lake Urmia watershed climate is semi-arid and cold. The average annual rainfall of the watershed is 337.1 mm.

  6. 6.

    The Persian Gulf–Oman Sea extends in a northwest–southeast direction along with the Zagros mountain range with nine sub-basins. The area covered by the watershed is 432,390 km2. The climate of this watershed varies from the cold and semi-arid climate in the north, warm and semi-arid in the middle, and warm and humid climate in the south. The average annual rainfall is 365 mm, which decreases from northwest to southeast. Mountainous areas occupy 65% of watershed and the remaining 35% by plains (MEI 2018).

Fig. 2
figure 2

Geographic distribution of 44 stations used in six studied watersheds

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In this study, monthly precipitation and temperature data of 44 synoptic stations from 1989 to 2018 were used. The spatial distribution of the stations in the watersheds is shown in Fig. 2. The run test method (Lazaro et al. 2001) was applied for examining the homogeneity of precipitation data.

Methodology

The research methodology is comprised of the following steps (Fig. 3):

  1. 1.

    In the first step, to understand the relationship between DS and precipitation characteristics in Iran, the average annual precipitation (Fig. 4a) and the coefficient of monthly precipitation (Fig. 4b) (1989–2018) were calculated.

  2. 2.

    The SPI was calculated on a monthly scale (1989–2018) to determine DS and find its spatial–temporal variability.

  3. 3.

    Using the Hurst exponent, the persistence percentage of DS was calculated with the monthly values obtained from the SPI. The purpose of using this index is to find the pattern and direction of the long-term spatial and temporal variability of DS.

  4. 4.

    To find the relationship between persistence and spatial–temporal variability, the frequency and severity of drought were interpolated on the seasonal and annual scales (1989–2018). Also, using the Mann–Kendall method, the trend of drought intensity was detected in Iran for three decades (1989–1998, 1998–2009, and 2009–2018).

  5. 5.

    The relationship between DS and ENSO is displayed in Figs. 11 and 12.

  6. 6.

    To compare the trend of DS and its persistence, the climatic diversity of Iran was identified using the dryland index calculated with monthly precipitation and temperature data.

Fig. 3
figure 3

Methodology steps

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Fig. 4
figure 4

The average annual precipitation (a) and coefficient of variation of monthly precipitation (b) in Iran from 1989 to 2018

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The Hurst exponent

The Hurst exponent is an index for understanding the long-term memory of a variable’s behavior in a time series (Sánchez Granero et al. 2008) and finding similarities in a time series (Chandrasekaran et al. 2019). Hurst (1951) introduced the Hurst exponent to study the hydrological complexities of the Nile River in Egypt. The non-random changes in the time series of the Nile River flow behaviors accompanied by high variability were the basis of the H exponent use (Sutcliffe et al. 2015). There are different ways to calculate the Hurst exponent. The rescaled range (R/S) analysis is based on the previous work of Hurst (1951), and the best-known method to calculate the Hurst exponent was suggested by Mandelbrot and Wallis (Sanchez Granero et al. 2008). The steps to calculate the rescaled range method are as follows:

Normalization of rainfall time series:

$$ {y}_i={X}_i-\overline{X} $$
(1)

Calculation of the cumulative time series:

$$ {z}_i={\sum}_{i=1}^i{y}_i\kern0.5em i=1,\dots, n $$
(2)

The range (RN) is set as the interval that a process moves in the time of the index N (Hurst 1951):

$$ {R}_N=\max \left({z}_1,{z}_1,\dots, {z}_n\right)-\min \left({z}_1,{z}_1,\dots, {z}_n\right)\kern1.5em {\left(\mathrm{R}/\mathrm{N}\right)}_N=C.{N}^H $$
(3)

where the subscript N for(R/N)N determines the duration of the individual short time series and C is a constant.

The H exponent is just the slope of the ordinary least square regression line equation obtained by plotting log(R/N)N versus log(N) as

$$ \log {\left(\mathrm{R}/\mathrm{N}\right)}_N=H\ \log\ C+H\log N $$
(4)

An H value closer to 1 indicates that a process is close to a state of persistence, and values less than 0.5 denote lack of persistence of the phenomena (Tatli 2015).

The standardized precipitation index

The SPI was first used by McKee et al. (1993) to study drought. The formula of the index is:

$$ \mathrm{SPI}=\frac{X-\overline{X}}{\mathrm{SD}} $$
(5)

X is precipitation, \( \overline{X} \) is mean precipitation, and SD is the standardized deviation of precipitation (Eq. 5).

The formulation of the SPI is based on the density and probability function gamma (McKee et al. 1993).

$$ f(x)={\int}_0^XF(X) DX=\frac{1}{\overline{\beta}\ \tau \left(\overline{\alpha}\right)}{\int}_0^X{X}^{\overline{\alpha}}{e}^{\frac{\overline{X}}{\overline{\beta}}} dx $$
(6)

where α is the form parameter (α > 0), β is the scale parameter (β > 0), and x is precipitation, with x varying according to α and β (Eq. 6) (Oliveira Junior et al. 2018). If x = 0, it should be modified by Eq. 7:

$$ H(x)=q+\left(1-q\right)G(x) $$
(7)

where q is probability of zero precipitation in data series. G is the gamma distribution of the cumulative probability function. According to the SPI, the drought severity categories are 0.99 to −0.99 (near normal), −1.00 to −1.49 (moderate), −1.50 to −1.99 (severe), and ≤ −2 (extreme) (McKee et al. 1993).

The Mann–Kendall test

The Mann–Kendall method as a non-parametric test was introduced and developed by Mann (1945) and Kendall (1975) and is a widely used tool for trend detection (Nyikadzino et al. 2020). The calculation steps are as follows:

$$ S=\sum \limits_{i=1}^{n-1}\sum \limits_{j=i+1}^n\operatorname{sgn}\left({x}_j-{x}_i\right) $$
(8)
$$ \operatorname{sgn}\left({x}_j-{x}_i\right)\left\{\begin{array}{ll}+1& \mathrm{if} \operatorname {sgn}\left({x}_j-{x}_i\right)>0\\ {}0& \mathrm{if} \operatorname {sgn}\left({x}_j-{x}_i\right)=0\\ {}-1& \mathrm{if} \operatorname {sgn}\left({x}_j-{x}_i\right)<0\end{array}\right. $$
(9)
$$ \mathrm{Var}(S)=\frac{n\left(n-1\right)\left(2n+5\right)-{\sum}_{i=1}^m{t}_i\left({t}_i-1\right)\left(2{t}_i+5\right)}{18} $$
(10)
$$ {Z}_s=\left\{\begin{array}{ll}\frac{S-1}{\sqrt{\mathrm{Var}(S)}}& \mathrm{if}\ S>0\\ {}0& \mathrm{if}=0\\ {}\frac{S+1}{\sqrt{\mathrm{Var}(S)}}& \mathrm{if}\ S<0\end{array}\right. $$
(11)

In Eq. 8, n is the number of data points; xi and xj are the data values in time series i and j (j > i), respectively; and sgn xj − xi is the sign of Eq. 9. Equation 10 is the variance, and m is the number of tied groups, and ti denotes the number of ties of extent i. A tied group is a set of sample data having the same value.

In cases where the sample size n > 10, the standard normal test statistic ZS is computed using Eq. 11. Positive values of ZS indicate increasing trends while negative ZS values show decreasing trends (Gocic and Trajkovic 2013). In this study, the Mann–Kendall test has been used to determine and compare the trend of seasonal and annual droughts.

The dryland index

To compare the severity of drought and aridity in Iran, the dryland index (P/PET) (Eq. 12) has been calculated (Fu and Feng 2014).

$$ \frac{P}{16K{\left(\frac{10T}{I}\right)}^m} $$
(12)

P is the annual average of precipitation. \( 16K{\left(\frac{10T}{I}\right)}^m \) is the Thornthwaite (1948) method for the calculation of potential evapotranspiration (PET). K is the correction coefficient calculated as a function of the latitude and month. I is a heat index and is calculated by the following formula:

$$ I={\sum}_{i=1}^{12}{\left(\frac{T_a}{5}\right)}^{1.514} $$
(13)

a is 0.49 + 0.0179 × I − 0.0000771 × I2 + 0.000000675 × I3. T is the average monthly temperature, and m is a coefficient depending on I (Eq. 13). Based on the United Nations Convention to Combat Desertification (1994) category, the dryland index identifies types of arid lands with values less than 0.65. Classification of aridity based on the dryland index are hyper-arid (<0.05), arid (0.05–0.2), semi-arid (0.2–0.5), dry-subhumid (0.5–0.65), and non-dryland (>0.65) (UNEP 1992).

Interpolation technique

In this study, the ArcGIS software and IDW (inverse distance weighting) technique have been used to show the spatial variability of PDS in dryland areas of Iran.

Results and discussion

The coefficient of variation of rainfall in drought severity in Iran

The average annual rainfall of Iran is 250 mm based on the precipitation records of 44 synoptic stations available from 1989 to 2018 (Fig. 4a). The temporal and spatial distribution of precipitation is not uniform in Iran (Fig. 4 a and b). Generally, there is a discernible relationship between the amount of precipitation and its coefficient of variation.

The average coefficient of variation of annual precipitation in Iran is 12% despite the rainfall amount being low (250 mm). Elevation and latitude are two important factors in the variability of rainfall in Iran and define the boundaries of semi-arid climates (Hejazizadeh et al. 2016). The humid and semi-arid regions of the country have the highest coefficient of variation, generally located in the Caspian coast and the Alborz (north) and the Zagros (northwest–southeast) mountain range areas. The Central Plateau and the East Boundary as the driest watersheds (arid climate) have the lowest coefficient of variation of precipitation, with an average annual rainfall of less than 200 mm. Previous studies have shown that there is a relationship between the amount of rainfall variability and the characteristics of droughts (Bonaccorso et al. 2003; Mucheru-Muna et al. 2015).

The aridity situation in Iran

The PET is highly variable due to climatic and geographical diversity in Iran. The maximum PET is found in the southern portion of the Persian Gulf–Oman Sea watershed. Also, areas with the minimum value are located in the north of Iran, where the average annual temperature is lower than those of the other parts of the country (Fig. 5a). According to Fig. 5b, which displays the dryland index (P/PET), the hyper-arid and arid driest areas of the country are in the Central Plateau and the East Boundary watersheds. The drylands vary in the Persian Gulf–Oman Sea watershed due to the Zagros Mountains range aligning in the northwest–southeast direction, water body in the south, and the arrival of rain systems including the Mediterranean cyclones (west) and low-pressures Sudanese (south). Also, areas located in the mountainous areas of the country are semi-arid areas. The dry-subhumid and non-dryland are scattered in small areas in the Caspian Sea and the Persian Gulf watersheds.

Fig. 5
figure 5

The annual potential evapotranspiration (a) and dryland area diversity (b) in Iran (1989–2018)

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Temporal and spatial variability of drought

Drought in Iran is a dominant hazard that affects large parts of the country every year. Since precipitation in Iran has a high spatial and temporal variability, droughts follow a similar distribution pattern. The general trend of rainfall in Iran is decreasing from north to south and from west to east. According to Fig. 5, the frequency of mild droughts is increasing from north to south. Unlike mild drought, moderate and extreme droughts increase from south to north. There is no specific trend for severe droughts, but they occur in the north, west, and middle of Iran most frequently. The highest intensity of drought corresponds to the high precipitation areas of the country.

Most of the country’s precipitation falls in winter, autumn, and spring, in that order. As can be seen, severe and extreme droughts in the Persian Gulf–Oman Sea and the Caspian Sea watersheds occurred more than the average (Fig. 6).

Fig. 6
figure 6

The average annual drought frequency based on the SPI category in the studied basins (a mild drought frequency, b moderate drought frequency, c severe drought frequency, and d extreme drought frequency) (1989–2018)

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The maximum frequency of mild droughts is located in the Central Plateau watershed. By comparing the maps in Figs. 4 and 6, it can be concluded that DS with the coefficient of variation of precipitation has a discernible relationship in the period of study (1989–2018). The highest coefficient of variation of monthly precipitation is observed in the Caspian Sea and the Persian Gulf–Oman Sea in the long term (1989–2018), the most humid watersheds, where the frequency of severe and extreme droughts is higher.

According to Fig. 7, 1- to 3-year-long drought durations are more frequent in all watersheds. The maximum durations of 1-year and 2-year droughts are prevalent in the Lake Urmia and the Caspian Sea watersheds, respectively. With increasing drought duration, the frequency of watersheds decreases. In the Central Plateau and the East Boundary with hyper-arid and arid climates, 3-year and 4-year droughts are more frequent, respectively. In the Persian Gulf–Oman Sea watershed, the maximum duration drought (8-year) occurred once.

Fig. 7
figure 7

Average drought duration based on the SPI (1989–2018)

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In arid watersheds and lowland areas, although the variability of rainfall is lower, the frequency of mild and moderate droughts is high with a longer duration. Conversely, in semi-arid, humid and, highland regions of watersheds, the rainfall variability and the frequency of severe and extreme droughts are higher but drought durations are shorter (Alijani and Fini 2009; Fini and Alijani 2013; Nabaei et al. 2019), so the cumulative effects of this risk are reduced. High evaporation intensifies droughts and increases the cumulative effects of DS (Hatefi et al. 2016; Rezaee et al. 2017).

Figure 8 shows the variability of DS during the period of 1989 to 2018 in the seasonal and annual scales based on the SPI. In general, winter is the highest precipitation season in the whole country with a lower drought intensity in the statistical period (1989–2018). The variability of DS in spring and annual is the same, but the spring droughts are more intense. Autumn droughts are more severe in the south Persian Gulf–Oman Sea watershed.

Fig. 8
figure 8

The severity of seasonal (a–c) and annual (d) droughts in the historical period (1989–2018)

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Figure 9 shows the average drought intensity in three different decades of the study period (1989–2018). In the first decade (1998–1998), the severity of the drought in the south is higher, and in the second decade (1999–2008), it is higher in the north of the country. In the third decade (2009–2018), the distribution of drought intensity does not show a specific spatial trend over the country but its intensity has increased significantly in the north and west.

Fig. 9
figure 9

The average of drought severity in the three decades. a 1989–1998. b 1999–2008. c 2009–2018

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The trend of drought severity in Iran

The trend of drought severity is very similar on winter and annual scales, although the severity of winter droughts is slightly higher (Fig. 10). The similarity between the trend intensity of winter and annual droughts shows that this season has a higher impact on the trend of long-term droughts. There is an increasing trend in DS in autumn in small areas of the Caspian Sea and the Central Plateau watersheds. An incremental trend in DS is observed in spring, including northwest, the Caspian coast, and the smaller area in the southern part of the country. The intensities of spring and autumn droughts are very similar, but in autumn, there is a more intense trend of increasing drought intensity. Note that a higher increasing trend of DS is found in the most humid areas in north and west regions of country (Fig. 10).

Fig. 10
figure 10

The trend of seasonal (a–c) and annual (d) droughts using the Mann–Kendall method (1989–2018)

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Relationships between PDS and the large climatic fluctuations

The large-scale atmospheric circulation indices could describe the pattern of rainfall variability (Luppichini et al. 2021; Sah et al. 2021; Zerouali et al. 2018) and regional droughts (Amini et al. 2020). In this study, Pearson correlation at the significance levels of 0.01 and 0.05 between the values of SPI, NAO (https://www.ncdc.noaa.gov/teleconnections/nao), and ENSO (https://www.ncdc.noaa.gov/teleconnections/enso/indicators/soi) in the studied stations was calculated in 1989–2018, and the output showed that ENSO has a stronger relationship with DS (Azizi 2000). Figure 11 shows the relationship between the average SPI and ENSO values in 1989–2018. Also, based on the results, the spatial and temporal distribution of the relationship between DS and ENSO is shown in Fig. 12. Expanding the impact of ENSO on the severity of droughts in Iran has high spatial and temporal changes that could intensify the variability of DS. The range of correlation between ENSO and SPI values varied from 0.441 to 0.517 at the 0.01 significance level and 0.312 to 0.417 at the 0.05 significance level. In February, there is a further expansion of the impact of ENSO, and November has been removed because no connection was found. There is a stronger relationship in the west and north from February to December, and it is limited to the east and south from April to June. In general, the severity of the drought has increased in the positive phases of ENSO (La Niña), and in the negative phases (El Niño), it is the opposite.

Fig. 11
figure 11

The average trend of drought severity in Iran and ENSO (1989–2018)

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Fig. 12
figure 12

Geographical distribution of the correlation between the severity of drought and ENSO in Iran (1989–2018)

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The persistence of drought severity (PDS) in Iran

For the H exponent, values greater than 0.5 show the persistence of drought conditions. In Iran, for all 44 stations, H values of DS are higher than 0.5 with an average of 0.78 (Fig. 13). These values confirm that droughts are a frequent and persistent hazard in Iran. In Fig. 13, the percentages of PDS are different due to the diverse climatic and geographical conditions in Iran. A higher variability of PDS values is observed in the Caspian Sea and the Persian Gulf–Oman Sea watersheds with higher participation and coefficient of variability in the long term (1989–2018). Also, the highest PDS values exist in the south Caspian Sea and the west Persian Gulf–Oman Sea, which are the most humid watersheds of the country. In the west part of Iran with a dry-subhumid climate, DS has increased in the third decade (2009–2018) and the same trend is also seen in the Caspian Sea watershed (Fig. 9). In general, in the Midwest and northwest of Iran, the intensity of PDS is small and increases toward the east. DS has reached a significant percentage of persistence, and it is important to note that this is the same for the whole country. According to Fig. 9, the spatial variability of drought intensity during the three decades has shifted from south to north (1989–1998) (Fig. 9a), north to south (1999–2008) (Fig. 9b), and non-uniformly (2009–2018) (Fig. 9c). Also, in the third decade (2009–2018) (Fig. 9c), the non-uniformity of the spatial trend of droughts has been accompanied by an increase in drought severity.

Fig. 13
figure 13

The persistence of drought severity (PDS) based on the SPI and the Hurst exponent in Iran (values are classified in 7 colors) (1989–2018)

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The existence of mountainous regions (Fig. 2) with high coefficients of variation of monthly precipitation (Fig. 4b) has not made PDS a specific trend, but in the middle parts of Iran from west to east, a discrete belt of severe PDS is observed (Fig. 13). In the Persian Gulf–Oman Sea and the Caspian Sea watersheds with dry sub-humid climate, two cores of extreme PDS with an increasing trend of drought intensity were detected in the third decade (2009–2018) (Fig. 9c). The coefficient of precipitation variation plays an important role in the PDS variability in Iran. There is an inverse relationship between the coefficient of rainfall variation and the PDS in the arid watersheds. In the semi-arid and humid watersheds, this relationship is positive linear. This finding is consistent with the other research works conducted with different methodologies. For example, by comparing precipitation fluctuations and DS between semi-arid and humid regions in Iran, Shiau and Modarres (2009) concluded that high precipitation variability increased DS more in the humid climatic zone of the country. PDS values in the study period are highly consistent with the trend of DS in the third decade (2009–2018) (Fig. 9c). The increase in drought intensity in the last three decades has been accompanied by a change in spatial trends. Lashkari et al. (2021) concluded that prolonged droughts (mega-droughts( have increased in Iran in recent decades.

As the distribution of altitudes in cold and semi-arid areas plays a role in the rainfall variation, they have also increased the variability of the PDS values. Goudarzi et al. (2018) estimated that the amount of evaporation would increase in Iran in the future, even in the cold and semi-arid regions. With change in the ratio of precipitation and evapotranspiration, dryland diversity also will change. Although the results show less PDS in the mountainous areas, simulations of climate change in some studies have shown that PDS in these areas will be more variable than the plains in Iran (Barzegari and Maleki 2016).

Climate change could make the PDS phenomenon even more complicated in the diverse climate and geography of Iran. Future work will focus on the relationship between large-scale atmospheric systems, climate change, and PDS.

Conclusions

Drought is one of the most important environmental hazards in Iran, which intensifies because of low precipitation. In addition to the short-term effects, drought threatens the sustainable development of socio-economic sectors of the country. This research was conducted to evaluate changes in DS in Iran using the Hurst exponent and the SPI. Drought in Iran is a frequent hazard with high variability due to the diversity of geographical and climatic conditions. By comparing the spatial and temporal of DS trends and its persistence values, the H exponent shows the long-term pattern of its variability. According to Fig. 5, Iran is diverse dryland with an arid climate in the eastern part and a semi-arid climate in the western area. The gradual decrease in rainfall from west to east and north to south has also affected the characteristics of the drought. Tatli (2015) mentioned the study of drought persistence as a valuable method to predict and find atmospheric patterns in a drought event. Also, spatial–temporal variability was observed in the relationship between DS and ENSO. In this study, the findings demonstrate that the pattern of spatial and temporal variability of drought is consistent with the long-term trend of PDS. Overall, the results confirm that the H exponent is a useful method for tracking the spatial–temporal trend of drought severity.