1 Introduction

Extreme precipitation is the subject of extensive research based on many indices and methods (Alexander et al., 2019; Donat et al., 2013, 2017). Any changes in extreme precipitation and its contribution to the annual precipitation profoundly affect the natural environment and human society. It can affect water resources (Cardoso Pereira et al., 2020), the environment (Prein et al., 2017), agriculture (Carpenter et al., 2018), socioeconomic systems (Zhang et al., 2018), and health (IPCC, 2012).

Extreme precipitation-related natural disasters have increased in recent years. About 90% of natural disasters are caused by climate hazards such as floods, droughts, and heat stresses (UNISDR, 2015). In general, spatial extents of precipitation are heterogeneous, which favors many changes in different climate regimes. Therefore, it is essential to study the characteristics of the trend, such as the intensity and change-point of precipitation and its contribution to the total annual precipitation in different regions of the world (Rahman & Islam, 2019; Trenberth et al., 2003).

Based on the latest reports of the Intergovernmental Panel on Climate Change (IPCC) in the Fifth Assessment Report (IPCC, 2013) and a special report on the impacts of global warming of 1.5 °C (Masson-Delmotte et al., 2018), global warming has increased the frequency, intensity, and duration of extreme precipitation events. Extreme precipitation has intensified in different regions, and RX1day has risen at about two thirds of the world’s stations (Donat et al., 2013, 2019; Westra et al., 2013). Extreme climate events and their variations are crucial to human and natural society due to their potentially severe effects, as stated in the Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX) (IPCC, 2012).

The Middle East region is a climate change hotspot in which precipitation events are expected to increase and intensify for all seasons (Tabari & Willems, 2018). Iran is one of the driest regions in the Middle East, with an average annual precipitation of about 250 mm (Javanmard et al., 2010), and has notable climate diversity in terms of spatiotemporal precipitation regimes. However, a significant amount of total annual precipitation falls during the cold period of the year. Geographically, the southern coast of the Caspian Sea and the mountainous regions of Iran receive the most considerable amount of precipitation (Alijani et al., 2008). In addition, the contribution of extreme precipitation to total precipitation in Iran is substantial.

The spatiotemporal distribution and precipitation trend in Iran have been studied by numerous researchers in recent years (Alijani et al., 2008; Ghalhari et al., 2016; Khalili et al., 2016; Najafi & Moazami, 2016; Salehi et al., 2020; Some'e et al., 2012; Zarrin & Dadashi-Roudbari, 2021). These studies have shown a decreasing precipitation trend in most parts of Iran. However, according to climate projections, extreme precipitation and the frequency of consecutive dry days are likely to increase in the future (Hay et al., 2016). Therefore, examining the extreme precipitation variabilities provides essential results for interpreting possible future trends.

Climate extremes, especially extreme precipitation, are the subject of particular research. This includes global studies (Donat et al., 2013, 2017 and 2019; Alexander et al., 2019), continental Asia (Kirschbaum et al., 2020), Africa (Shongwe et al., 2011), North America (Kunkel, 2003), South America (Palharini et al., 2020), and Australia (Wasko et al., 2018). In addition, this topic receives special attention on the regional scale (Dravitzki & McGregor, 2011; Guo et al., 2018; Heureux et al., 2022; Li et al., 2015; Talchabhadel et al., 2018).

Many researchers have analyzed he extreme precipitation in the region of the Middle East, including Iran (de Vries et al., 2013; Tabari & Willems, 2018; Zhang et al., 2005). Overall, these studies may group into two categories: (1) across Iran (Alavinia & Zarei, 2021; Darand et al., 2017; Mahbod & Rafiee, 2021; Najafi & Moazami, 2016; Rahimi & Fatemi, 2019; Rahimzadeh et al., 2009; Soltani et al., 2016; Tabari et al., 2014) and (2) some specific regions of Iran (Kiany et al., 2020). Some studies have examined the synoptic patterns associated with extreme precipitation events (Rousta et al., 2020; Shaffie et al., 2019).

Despite many works that reviewed extreme precipitation over Iran, two aspects of them have received less attention. Most of the studies conducted for precipitation extremes only used 95th and 99th percentiles of precipitation in Iran (Fathian et al., 2020; Ghiami-Shamami et al., 2019; Rahimi & Fatemi, 2019; Rahimzadeh et al., 2009; Soltani et al., 2016). We have used the new Expert Team on Sector-specific Climate Indices (ET-SCI) recommended by the World Meteorological Organization (WMO) along with the Expert Team on Climate Change Indicators Detection and Indices (ET-CCDI). The most recent research that investigated extreme precipitation in Iran (Alavinia & Zarei, 2021; Mahbod & Rafiee, 2021) has examined only percentile indices, and they did not focus on ETCCDI. Also, no study has investigated the contribution of extreme precipitation to total precipitation in Iran.

Compared to similar studies conducted on extreme precipitation in Iran, this research investigates the new indices recommended by ET-SCI, detects the extreme precipitation time series change-point, determines the contribution of extreme precipitation to total annual precipitation, and finally applies the modified Mann–Kendall for trend detection. Extreme precipitation and its contribution to total annual precipitation in recent decades in Iran has shown complex variability. Therefore, this study aims to analyze extreme precipitation to distinguish the contribution of the leading precipitation indices to the total annual precipitation in Iran.

This paper provides a comprehensive extreme precipitation analysis in Iran, which is organized into five main sections. Section 1 presents an investigation of Iran's extreme precipitation based on the recommended indices of ET-SCI and ETCCDI. Section 2 presents computation of the trend and slope estimator of extreme precipitation studied based on the modified Mann–Kendall and Sen methods. Section 3 presents attempts to detect the change-point of Iran extreme precipitation. Section 4 presents an investigation of the contribution of extreme precipitation to total precipitation, and Sect. 5 presents calculation of cross-correlation extreme precipitation indices (EPIs) in Iran. Comparing the findings of this paper with the results of previous studies (such as Alavinia & Zarei, 2021; Mahbod & Rafiee, 2021; Rahimi & Fatemi, 2019) will improve our knowledge of extreme precipitation and provide a better interpretation of its changes.

2 Material and Methods

2.1 Description of the Study Area

Iran, located between 25°30′N to 39°47′N and 44°5′E to 63°18′E, with a predominantly hot and dry climate, has a variety of climates ranging from Cfa to Bwh based on Köppen–Geiger climate classification. Accordingly, climatic diversity is evident in the spatiotemporal distribution of precipitation. In this research, we aim to investigate extreme precipitation in different climate zones of Iran. For this purpose, we used the Köppen–Geiger climate classification method. Of the 31 Köppen–Geiger climate calss, 13 are reorganized in Iran (Fig. 1). The predominant climates of Iran are desert (BW, in the east and southeast of Iran) and semi-desert (BS, in the northeast of Iran), and the temperate climate is limited to small parts of the Zagros and the southern coast of the Caspian Sea (Zarrin & Dadashi-Roudbari, 2021). We selected 49 synoptic stations with long-term records (1980–2019) in seven climate zones including Bsh (three stations), BsK (12 stations), BWh (15 stations), BWk (eight stations), Cfa (one station), Csa (five stations), and Dsa (five stations).

Fig. 1
figure 1

a) Location of ground stations used in this study. Shaded color represents topography. b) Köppen–Geiger climate classification [0.0083° resolution (approximately 1 km at the equator)] (Beck et al., 2018)

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2.2 Selection of Synoptic Stations

Extreme precipitation is statistically infrequent, and the study of the characteristics of these precipitation events and the determination of their trend is closely related to the accuracy of daily data and missing values. Daily precipitation data used in this study were obtained from the Iran Meteorological Organization (IRIMO). There are 414 synoptic stations in Iran, of which only 50 stations have 40-year long-term records (1980–2019). Therefore, selected stations in this study were examined for completeness, quality, and homogeneity.

2.3 Completeness

Stations containing missing values for more than 10% (Zolina et al., 2005) of their total daily time series (1980–1920) were removed from the data set. The lack of more than 10% in the selected time series is not acceptable due to the sensitivity of the linear trend of daily precipitation time series. Accordingly, Hamedan (Nozheh), Dezful (Airport), Omidiyeh (Air Base), Omidiyeh (Aghajari), Tabas, and Bushehr (Coastal) stations were removed from the data set. Finally, 49 stations were selected for a statistical period of 40 years (Fig. 1).

2.4 Quality Control

To identify suspicious data from a 40-year time series, two conditions were used for this purpose (Ghiami-Shamami et al., 2019; Mahbod and Rafiee, 2021; Soltani et al., 2016): (1) data with more than three standard deviations from daily values; and (2) duplicate data of more than 10 days with nonzero values. Applying the above two conditions for the time series of 49 selected stations in Iran does not show this, so the quality of the data is approved.

2.5 Homogeneity

As mentioned, after applying the quality control criteria and completeness of the data from 55 stations, six stations were left out. Based on this, 49 synoptic stations with complete and homogeneous data were selected (Fig. 1). As shown in Fig. 1, the selected stations with appropriate spatial distribution are scattered throughout Iran, and the homogeneity of these data is confirmed at α = 0.05.

2.6 ETCCDI and ET-SCI Indices of Precipitation Extremes

There are several ways to study climate extremes. Some studies look at extraordinary or record-breaking events over a certain time frame (Beniston, 2015), and many studies look at absolute thresholds or percentiles. Leander et al. (2014), Schär et al. (2016), and many other studies use extreme value theory (EVT) to compute return periods (Kharin et al., 2013; Tebaldi & Wehner, 2018). To facilitate the analysis of temperature and precipitation extremes, the new ET-SCI recommended by the WMO along with the ET-CCDI has defined a set of climate change indices focusing on extreme events. These indices generally describe extreme events, with a time step of 1 year or less (Zhang et al., 2011) widely used in IPCC reports (Hoegh-Guldberg et al., 2018; IPCC, 2012; Stocker et al., 2013). In this study, we used 12 extreme precipitation indices in three groups of duration, frequency, and intensity from ETCCDI and ET-SCI (Table 1).

Table 1 List of selected extreme precipitation indices (EPIs) (adapted from ET-SCI) (Chapagain et al., 2021)
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3 Statistical Methods

3.1 Calculation of Extreme Precipitation Trend [Modified Mann–Kendall [MM–K])

The modified Mann–Kendall (MM–K) test was used to analyze the trend analysis in the long-term data series. In this test, H0 indicates the absence of a trend, and H1 indicates the trend in the time series of data (Mann, 1945; Kendall, 1948). The Z score in the MM–K test follows the standard normal distribution with an average of zero and a variance of 1 and is used to measure the trend (Liu et al., 2014). It should be noted that the rejection of H0 in this test does not mean that there is no trend in the time series. Instead, it shows that the available evidence is insufficient to conclude that there is no trend in the time series (Dadashi -Roudbari & Ahmadi, 2020; Maghrabi & Alotaibi, 2018).

The MK test statistic (S) of a data series, y having n data points, is estimated as (Mann, 1945)

$$ S = \mathop \sum \limits_{i = 1}^{n - 1} \mathop \sum \limits_{j = i + 1}^{n} sgn\left( {x_{j} - x_{i} } \right), $$
(1)

where

$$ sgn\left( {x_{j} - x_{i} } \right) = \left\{ {\begin{array}{*{20}c} 1 & {if} & {\left( {x_{j} - x_{i} } \right){ }} \\ 0 & {if} & {\left( {x_{j} - x_{i} } \right){ }} \\ { - 1} & {if} & {\left( {x_{j} - x_{i} } \right){ }} \\ \end{array} \begin{array}{*{20}c} { > 0} \\ { = 0} \\ { < 0} \\ \end{array} } \right\} $$
(2)

The variance of S [V(S)] is used to estimate Z statistics to decide trend significance:

$$ Z = \left\{ {\begin{array}{*{20}c} {\frac{S - 1}{{\sqrt {V\left( s \right)} }}} & {if} & {s > 0} \\ 0 & {if} & {s = 0} \\ {\frac{S + 1}{{\sqrt {V\left( s \right)} }}} & {if} & {s < 0} \\ \end{array} } \right\} $$
(3)

The MM–K test can be used only if Z is found to be significant in the Mann–Kendall (MK) test. The MM–K test evaluates whether the MK trend is due to the natural variability of climate or due to a global warming-induced unidirectional trend (Pour et al., 2020). The MM–K test de-trends the time series (Hamed, 2008).

The significance of H is decided by Pour et al. (2020) by the use of first and second moments for H = 0.5. For significant H, the variance of S is estimated as

$$V\left( S \right)^{\mathop H\limits } = \mathop \sum \limits_{i < j} .\mathop \sum \limits_{k < l} \frac{2}{\pi }sin^{ - 1} \left( {\frac{{\rho \left| {j - i} \right|\left. { - \rho } \right|\left. {i - l} \right|\left. { - \rho } \right|\left| {j - k} \right|\left. { + \rho } \right|i\left. { - k} \right|}}{{\sqrt {\left( {2 - 2\rho \left| {i - j} \right|} \right)\left( {2 - 2\rho \left| {k - l} \right|} \right)} }}} \right) $$
(4)

Here, \( V\left( S \right)^{{{\text{ }}H}} \) is the biased estimate of the variance of S which can be eliminated through the use of a correction factor (B):

$$ V\left( S \right)^{H} = V\left( S \right)^{\mathop H\limits } \times B $$
(5)

The significance of the MM–K test is determined by using \(V{(S)}^{H}\) instead of V(S) in Eq. (4).

3.2 Calculation of the Trend Slope of Precipitation Extremes (Nonparametric SSE Test)

The nonparametric Sen's slope estimator (SSE) method can estimate the actual trend slope in the time series (Yue & Hashino, 2003). This method was first proposed by Theil (1950) and then developed by Sen (1968). We used the SSE method to estimate trends in extreme precipitation. Mathematically, it is represented as Eq. 6:

$$ Q = {\text{median}}\left[ {\frac{\Delta y}{{\Delta t}}} \right] $$
(6)

where \(\Delta y\) is the change of recorded values due to change time, and \(\Delta t\) is between two successive data points in the time series (Pour et al., 2020).

3.2.1 Nonparametric Change-Point Detection (Buishand)

In this study, the change-point of extreme precipitation was investigated using the nonparametric Buishand test (Buishand, 1982). The change-point is when the time series of the data previously has a definite distribution with a mean γ0 and for subsequent years has a definite distribution with a mean γ1. The point estimator is used to detect abrupt changes between two consecutive differences. In the Buishand test, the null hypothesis, H0 indicates the absence of a change-point in the time series, and H1 indicates the existence of a change-point in the data series used at an unknown point.

$$ S_{0} = 0,S_{k}^{*} = \mathop \sum \limits_{i = 0}^{k} \left( {x_{i} - \mu } \right),k = 1,2, \ldots ,T $$
(7)
$$ S_{k}^{{**}} = \frac{{S_{k}^{*} }}{\sigma } $$
(8)
$$ Q = 0 \le \mathop{^{max}_ { k}} < T^{{\left| {S_{k}^{{{\text{**}}}} } \right|}} $$
(9)

where, S refers to statistics of data homogeneity, and if they are close to zero, the data series are homogenous. \({{\varvec{x}}}_{{\varvec{i}}}\) = time series values. \({\varvec{\upmu}}\) = arithmetic mean of time series values of the desired parameter. \({\varvec{\upsigma}} = \) standard deviation of time series. \({\varvec{T}} = \) time; and \({\varvec{Q}} = \) critical values of the test that can vary from zero to infinity (Dadashi-Roudbari & Ahmadi, 2021). In the present study, the significance of the Buishand result was tested at the 95% confidence level using the Monte Carlo method.

3.3 Spearman's Rank Correlation Coefficient

Spearman's rank correlation coefficient was used to examine the relationship between the extreme precipitation indices. Spearman's method is one of the nonlinear methods for analyzing climate variables. Spearman's rank correlation test fluctuates between +1 and −1 (Myers & Sirois, 2004).

4 Results and Discussion

4.1 Percentile-Based Extreme Precipitation

In Iran, the maximum values of R95pTOT and R99pTOT were experienced in the Csb, Csa, and Dsa climate zones (Fig. 2). Geographically, these areas include the Caspian Sea coasts in northern Iran and the Zagros Mountains in western Iran, while the smallest values (less than 20% for the R95pTOT index and less than 5% for the R99pTOT index) for both the R95pTOT and R99pTOT spread in the BWh and BSk climates, especially in central Iran, southeast, and the coasts of the Oman Sea. The values of R95pTOT [14.80 to 31.76%] and R99pTOT [2.39 to 10.43%] indices are decreasing from north to south and west to east of Iran.

Fig. 2
figure 2

Spatial distribution of extreme precipitation indices (EPIs) recommended by the Expert Team on Sector-Specific Climate Indices (ET-SCI) in Iran (CDD [unit = day], CWD [unit = day], R10mm [unit = day], R20mm [unit = day], R30mm [unit = day], SDII [unit = mm/day], RX1day [unit = mm], RX3day [unit = mm], RX5day [unit = mm], PRCPTOT [unit = mm], R95pTOT [unit = mm] and R99pTOT [unit = mm])

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The trend of the R95pTOT index at 51.02% of the stations is increasing, but at only 4% of the stations is it statistically significant at the level of 0.05. At 48.98% of the stations, the trend is decreasing, but at only 4.16% of them is it significant at the level of 0.05 (Fig. 3). The R95pTOT index has shown an increasing trend in the mountainous regions of Iran but a decreasing trend in the arid regions of eastern Iran and the interior. So we can conclude that contribution from very wet days in the mountainous regions of Iran has increased in recent years. On the other hand, the R99pTOT has a decreasing trend in all areas of Iran, except for a few stations in the northwest, west, and northeast of Iran, where the contribution from extremely wet days in Iran is decreasing. Rahimzadeh et al. (2009) reported a similar trend for R95 throughout Iran from 1951 to 2003. A comparison of trends with the study of Rahimzadeh et al. (2009) shows that the changes in precipitation in Iran have increased over the last six decades. In Fig. 3, unlike the Csa climate zone, the R95pTOT and R99pTOT trends show a significant increase (the maximum Z score of the MM–K test for R95pTOT is 2.36, which is statistically significant at 0.05).

Fig. 3
figure 3

Annual trends of extreme precipitation indices over Iran in 1980–2019 (triangles = increasing trend; upside-down triangles = decreasing trend; inside black dot = significant trend at 95%)

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A critical point about precipitation in the northeast of Iran is the decreasing trend for most indices. These decreasing trends, even for annual precipitation, pose a severe threat to the water resources of northeastern Iran, the Karakum Basin, and the Atrak River.

The coefficient of variation (CV) in the three climate zones of BSh, Cfa, and Csa is positive for both precipitation percentile indices. The CV of R99pTOT in the Cfa climate zone has reached 97.55% in the last four decades. The coefficient of variation of these two indices in the BWh climate zone is entirely decreasing. In the BSK and Dsa climate zones, the CV of R95pTOT is positive, and R99pTOT is negative, and vice versa in the BWk climate zone.

Of the seven Köppen–Geiger climate classifications for which a representative station exists, the R95pTOT trend is increasing in five climate zones and decreasing in only two climate zones, BWh and BWk. For the R99pTOT index, the average trend is increasing in four zones and decreasing in three zones. Another important factor regarding the extreme precipitation in Iran that has not been addressed so far is the contribution of extreme precipitation indices in the total precipitation of the country.

The contribution of the R95pTOT index in Iran precipitation (Fig. 4) varies between 1.39 and 29.38%. The central and southeastern regions of Iran have the highest contribution of 95th percentile in annual precipitation, so about one third of the total precipitation in these regions includes precipitation with a 95th percentile threshold. In climate zones, the BWh with 16.26% has the highest contribution to the R95pTOT index in annual precipitation, and the Cfa with 1.35% has the lowest contribution in total annual precipitation (Table 2).

Fig. 4
figure 4

The contribution of precipitation extremes to annual total precipitation (ATP) (1980–2019) in Iran (unit = percent)

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Table 2 Mean, coefficient of variation (CV), trend using the nonparametric modified Mann–Kendall (MM–K) test, and trend magnitude based on Sen's slope estimator (SSE) for EPIs in different climate zones of Iran
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Among the 49 stations, only Chabahar and Gorgan detected a change-point for R95pTOT, and Bam, Chabahar, and Khorramabad detected a change-point for R99pTOT (Table 3). The values of these two indices forz the abovementioned stations are higher after the change-point than before the change-point which shows a significant upward trend of precipitation among these stations.

Table 3 The change-point in precipitation extremes using Buishand’s test
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4.2 Maximum 1-day, 3-day, and 5-day Precipitation

The average RX1day, RX3day, and RX5day for 49 selected stations for Iran reached 38.80, 54.62, and 60.98 mm, respectively (Fig. 2). These indices showed big changes in the arid climate. As seen in Table 2, the CV of RX1day and RX3day in the BSh climate zone was more than 50%. The variability of these three indices is widespread in Iran; the maximum values for RX1day and RX3day in Iran go with Cfa, Csa, and Dsa climate zones. In the Cfa climate zone, the land–sea interaction, the Dsa climate, and the wind effect of the Zagros Mountains play a vital role in increasing extreme precipitation. The highest Rx indices are related to the Cfa climate zone located on the southwestern coast of the Caspian Sea. The average RX1day, RX3day, and RX5day indices in the Cfa climate zone are 113.52, 191.21, and 225.31 mm, respectively (Table 2).

The Csa climate, which includes the coastal region of the Caspian Sea and the highlands of the Zagros mountains, is the second-most rainy climate zone in Iran. In the Csa climate, the average precipitation for the two indices of RX3day and RX5day is more than 100 mm. The CV of Rx indices in Cfa and Csa climatic zones is positive. In general, in the arid climatic zones of Iran, the contribution of RX1day, RX3day, and RX5day in ATP is higher than in other zones.

In general, all three indices decreased from west to east according to the topography in Iran. The contribution of RX3day in ATP varies from 6.43% in the Cfa climate zone to 35.03% in the BWh climate zone (Fig. 4). In general, in the arid climate zone, the contribution of RX1day, RX3day, and RX5day is higher than in other zones (Fig. 5).

Fig. 5
figure 5

Annual magnitude of the trend of extreme precipitation indices over Iran in 1980–2019 (triangles = increasing trend, upside-down triangles = decreasing trend) (year −1)

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In general, all three indices decreased from west to east in Iran. The contribution of RX3day in ATP varies from a minimum of 6.43% in the Cfa climate zone to a maximum of 35.03% in the BWh climate zone (Fig. 4). In general, in the arid climate zone, the contribution of RX1day, RX3day, and RX5day is higher than in other zones. Applying the MM–K test to selected stations for RX1day, RX3day, and RX5day indices, a significant trend with high oscillation was observed (Fig. 3); therefore, this value of both decreasing and increasing significance is seen less than other precipitation indices.

Examination of station trend changes for RX1day, RX3day, and RX5day indices showed that the Caspian coast and the Zagros mountain chains have the highest increasing trends. A significant increasing trend is evident for the RX1day, RX3day, and RX5day indices, which are 13.63, 5, and 10.52%, respectively. On the other hand, as mentioned before, the trend of precipitation indices in Iran experiences many regional changes, so the extreme indices in inland and eastern regions of Iran showed a decreasing trend due to the decrease in precipitation in recent years. A significant decreasing trend is computed at the level of 0.05 for RX1day at 11.11%, RX3day at 10.34%, and RX5day at 10% of all stations.

Computed trends in climate zones are essential in several aspects. The increasing trend of extreme precipitation in the northern climate zones (Csa and Cfa), which have a humid climate, creates wetter conditions. This increase is consistent with the “wet gets wetter” theory by Tan et al. (2015). Since part of the precipitation on the Caspian Sea coast is related to convection, it is not unreasonable to expect that these changes are organized in connection with the spatial pattern of changes in the frequency of deep convection. On the southern coasts of Iran, an increasing trend was seen for the three Rx indices. Rahimzadeh et al. (2009) reported significant wet conditions in the coastal areas of the Caspian Sea and the Persian Gulf and dry conditions in the western regions of Iran between 1951 and 2003, which was also confirmed by Mahbod and Rafiee (2021) using a rain gauge data set.

Based on the Modified Mann–Kendall (Fig. 3) and Sen slope (Fig. 5) tests, we find that RX1day decreases at more than half of the stations during the period 1980 to 2019. Stations with higher positive trends are located in the north and west of Iran, while a significant part of eastern stations in Iran detected negative trends (Fig. 3). This trend coefficient is comparable to the research of Fathian et al. (2020) and Soltani et al. (2016) which also reported a similar trend for Iran's extreme precipitation. The RX1day index has an increasing trend in four climate zones: Dsa, Csa, Cfa, and BSh. Also, at the station scale, at 44.89% of the stations, this extreme index has shown an increasing trend, which is 13.63% of all stations.

Westra et al., (2013) showed that 64% of Earth stations had an upward trend for the RX1day index. Comparing stations with an increasing trend in Iran with the global distribution increases the confidence that precipitation changes in Iran follow a general pattern on the Earth rather than being influenced by local factors. This result refers to the emergence of climatic signals in Iran. The trend of Rx indices is decreasing in parts of western and northwestern Iran (Lake Urmia basin). This decreasing trend was observed in the two mentioned regions with slight changes for all 12 extreme indices, indicating dry conditions in western and northwest Iran. Climate change has played a significant role in the drying up of Lake Urmia, along with an anthropogenic factor. The trend of RX1day, RX3day, and RX5day is increasing in the northeast and east of Iran. The magnitude trend (Z-score of the MM–K test) of −2.52 was computed for the RX5day index in Mashhad and Zabol, which is significant at the level of 0.05.

The change-point of the Rx indices is presented in Table 3. The RX1day index in two coastal stations in southern Iran at Bushehr (difference before and after the change-point of 12.18 mm) and Chabahar (difference before and after the change-point of 30.23 mm) had a change-point in 2001 and 2006. The difference in precipitation before and after the change-point shows an increasing trend for this EPI in these two regions of Iran. In contrast, the RX5day index decreased, in which the two stations of Mashhad and Shahroud had a significant change-point at the level of 0.05 in 1999 and 1996. The difference before and after the change-point in Shahroud is  −15.03 mm. The RX3day index also had a change-point for 1993 and 1996 at Nowshahr (Caspian Sea coast) and Shahroud stations. The index values in Shahroud are decreasing, and it is increasing for Nowshahr.

4.3 Heavy and Very Heavy Precipitation Days

The three indices of R10mm, R20mm, and R30mm for 1980–2019 were examined to investigate heavy and very heavy precipitation (Fig. 2). The hotspot of all three indices of heavy precipitation is on the Caspian Sea coast and then western Iran, which is located in the Csa, Cfa, and Dsa types of climate zone. The range of heavy and very heavy precipitation varies between 0.05 and 48.26 days across Iran.

The days with heavy and very heavy precipitation in the BSk, BWh, and BWk climate zones decreased in recent years. The highest decreasing trend of R10mm is seen in the Dsa climate zone with  −0.10 days/year (Fig. 4). Heavy precipitation days (R10mm) in 73.47% of all stations have a decreasing trend, and this decreasing trend at 25% of them is significant at the 0.05 level (Fig. 3 and Table 2).

Also, the R10mm index has shown a decreasing trend in all climate zones. Very heavy precipitation indices of R20mm and R30mm have a decreasing trend at 63.27% (in 12.90% of the stations, the trend is significant at the level of 0.05) and 57.15% of the stations in Iran, respectively.

Of the three indices used to study the changes in heavy and very heavy precipitation in Iran, only two indices, R10mm (heavy precipitation) and R20mm (very heavy precipitation), had a change-point in the time series of the last four decades. In this regard, the number of stations with a change-point for the R10mm index is much higher, and 22.44% of stations show a significant change-point at the level of 0.05. The stations with change-points for heavy and very heavy precipitations are seen on the southern coasts (Chabahar, Bandar-e-Jask, Kish Island, Bandar Lengeh), west (Kermanshah, Khorramabad, Saqqez, and Sanandaj), northeast (Mashhad), the southern slopes of Alborz Mountains (Shahroud), and Shiraz station in the southwest of Iran (Table 3). Investigating the heavy precipitation change-point, it is found that most of the stations that show a change-point are located in western Iran. The difference between the average values of R10mm before and after the change-point in Khorramabad is  −5.20 days, Sanandaj  −5.85 days, and Saqqez  −4.90 days. Similar to R10mm, the change-point of the very heavy precipitation index (R20mm) is seen in the four stations of Kish Island, Bandar Lengeh, Saqqez, and Sanandaj, with the average R20mm changes of −2.36 and −2.38 days before and after the change-point, respectively.

4.4 Precipitation Intensity and Total Wet-Day Precipitation

The spatial distribution of the simple daily precipitation intensity index (SDII) shows that the precipitation intensity has increased uniformly in all climate zones of Iran in the last four decades (Table 2), as in many parts of the world (Kharin et al., 2018; Tabari, 2020).

Based on the results, the CV of SDII has increased in all climate zones of Iran. The CV for the climate zones of BSh, BSk, Bwh, Cfa, Csa, and Dsa has increased by 3.12, 25.81, 0.45, 53.5, 12.76, 17.65, and 8.19%, respectively. An increase in the intensity of precipitation and decrease in the annual precipitation can be seen in all climate zones of Iran (except Cfa, where annual precipitation has increased by 18.97%), especially in arid zones. The SDII showed an increasing trend in all climate zones of Iran from 1980 to 2019. However, only in the Cfa climate zone is the SDII index significant at the level of 0.05. The trend slope of the SDII in the mentioned zone is 0.05 mm/day/year (Fig. 5). SDII has a positive trend in 71.42% of stations, of which 22.58% of them are significant (α = 0.05).

The SDII change-point is significant in Bandar Anzali, Chabahar, and Sanandaj. These three stations are located in the southern Caspian Sea coast, the coast of the Oman Sea, and western Iran. Having the change-point of SDII in these three regions is very important, especially for the Chabahar station. This station is located in the semiarid region of Iran, and its total annual precipitation is about 120 mm; precipitation at this station has increased by 10 mm compared to before the change-point in 2006. This increase plays a vital role in flooding and soil erosion in this region. Precipitation in this region is affected by the Asian summer monsoon (ASM), so it seems that the ASM has strengthened in recent years, which could be due to changes in the large-scale atmospheric circulation under global warming. The trend of PRCPTOT is decreasing in all climate zones except for Cfa, which is increasing. The maximum changes in PRCPTOT in Iran were related to Dsa and BSh climate zones at 2.89 and 2.71 mm/year, respectively. However, the trend slope (Fig. 5) is not significant (α = 0.05).

4.5 Consecutive Wet Days (CWD) and Consecutive Dry Days (CDD)

The CWD index ranges from 2.24 days in southeastern Iran to 8.55 days on the southern Caspian Sea coast of Iran (Fig. 2). The CWD has a decreasing trend with a steep slope from northwest to southeast Iran. The hotspot of CWD in Iran is in the climate zones of Cfa, Csa, and Dsa. The CWD has a decreasing trend in all climate zones, except the Cfa which showed an increasing trend with 0.04 days/year (Fig. 5).

The CWD at 73.47% of the studied stations showed a decreasing trend, of which 13.88% were significant (α = 0.05).

The study of CWD for Birjand, Chabahar, Saqqez, and Shiraz has shown a significant change-point; the average CWD after the change-point was less than before the change-point. The CWD has decreased by 1 day during the last four decades (Table 3). The contribution of the CWD index in Iran is between 0.61 and 2.34% of the total days of the year. For example, 2.34% of the total days of the year in Bandar Anzali on the southwest coast of the Caspian Sea are consecutively wet days.

CDD is precisely the opposite of CWD, so the minimum average of the country with 30.14 days/year has been seen on the southwest coast of the Caspian Sea, and the maximum index of 213.70 days/year is detected in southeastern Iran.

Above 36° north, CDD is less than 50 days/year, and below 36° N in all regions of Iran, CDD is more than 100 days/year. Similarly, the contribution of CDD above 36° N is less than 10%, and below this latitude, it reaches a maximum of 58.54%. A critical and worrying point is the increase of consecutive dry days in wet areas of Iran such as Cfa and Csa so that consecutive dry days in the Cfa zone (Anzali in the southwest of the Caspian Sea) have increased by 35% over the last four decades. In the whole country, consecutive dry days in 46.93% of Iran have shown an increasing trend. A decreasing CDD and simultaneously increasing CWD in BWh, BWk, and Csa climate zones means increasing the amount of heavy precipitation in these climate zones of Iran. Also, at 10.26% of the stations, CDD is decreasing, and CWD is increasing simultaneously.

4.6 Cross-Correlation Extreme Precipitation Indices (EPIs) in Iran

To better present the relationship between extreme precipitation indices in Iran, a cross-correlation and scatter plot correlation matrix was prepared using the Spearman rank correlation method and is presented in Table 4 and Fig. 6. The correlation between extreme precipitation indices (EPIs) in Iran is between  −0.263 and 0.959. A strong negative correlation is between CDD and SDII, which is not significant (α = 0.05). In contrast, the strong positive correlation, which is significant at the level of 0.05, is between the two indices of RX5day and RX3day. PRCPTOT, RX1day, RX3day, and RX5day indices showed a strong correlation with EPIs. PRCPTOT has a significant and robust correlation with all EPIs at 95%, except for CDD and SDII in Iran. Thus, EPIs may reflect PRCPTOT changes in Iran to some extent. Ajjur and Riffi (2020) achieved a similar result in the Gaza Strip for EPIs. The Spearman rank correlation coefficient for RX1day, RX3day, and RX5day indices with PRCPTOT index was computed as 0.56, 0.57, and 0.58, respectively. However, some indices are different in terms of correlation relationships.

Table 4 Correlation matrix between indices of precipitation extremes in Iran
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Fig. 6
figure 6

Scatter plot correlation matrix EPIs in Iran. Each row and column represent an extreme precipitation index, and diameter histograms represent changes in that index throughout the year

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The CDD index has negatively correlated to all EPIs in Iran. However, this correlation is not significant for any of them. Spatial analysis of CDD and SDII correlation has shown that in transitional areas from a humid climate zone to a dry one, this relationship is more robust (for example, stations located on both sides of the Zagros or north and south Alborz). Also, there is a strong and positive correlation between precipitation intensity indices (RX1day, RX3day, and RX5day) with heavy precipitation indices (R10mm, R20mm, and R30mm); the Spearman rank correlation test coefficients between RX1day and R30mm in Iran show 0.62, which is significant at the 95% confidence level. Specifically, among 21 stations, R10mm has also increased by 38.09% with the increase of the RX1day index.

With an increase of precipitation days by more than one mm, the frequency of heavy precipitation increases in Iran. The R10mm index has no significant correlation with precipitation intensity. In contrast, the RX5day index has a crucial role in precipitation intensity (SDII) in Iran; the correlation value is 0.661, significant at the 95% confidence interval. The consecutive wet day index (CWD) shows a significant positive correlation with all EPIs, except for CDD and SDII. The strong correlation between R95pTOT and SDII (0.607) indicates that indices based on precipitation percentile are subject to change with precipitation intensity in Iran. In general, duration-based EPIs had a weak correlation with frequency indices and a strong correlation with intensity indices.

5 Conclusion

Compared to many studies that applied only 95th and 99th percentiles of precipitation (Alavinia and Zarei, 2021; Fathian et al., 2020; Ghiami-Shamami et al., 2019; Rahimzadeh et al., 2009; Rahimi & Fatemi, 2019; Soltani et al., 2016), new indices such as R30mm and RX3day and new combined index (100 * r95p or r99p / PRCPTOT) were used for detecting extreme precipitation in Iran. The 95th (99th) percentile is not a good index of precipitation intensity because the 95th (99th) index computes the percentage of daily precipitation events, whereas R95pTOT (99th) computes the total precipitation amount on rainy days when RR ≥ 95th (99th).

The results showed that the areas with high CWD are mainly located in the Caspian Sea coast and northwest and western regions of Iran, while the areas with CDD are mainly located in the central and eastern parts of Iran. The hotspot of heavy and very heavy precipitation indices and precipitation on days 1, 3, and 5 in Iran is located in the Cfa, Csa, and Dsa climate zones.

The consecutive wet day index (CWD), total precipitation on wet days (PRCPTOT), and heavy precipitation (R10mm) showed a decreasing trend of 73.47, 87.46, and 73.47% the in the last four decades, respectively.

The precipitation intensity index (SDII) and percentile-based indices (R95pTOT and R99pTOT) showed an increasing trend at 71.42, 51.02, and 57.14% of the total stations, respectively, during the last four decades. Globally, the increasing trend in precipitation event frequency under global warming (Benestad, 2018; Norris et al., 2019) has been confirmed.

The consecutive wet days (CWD), total annual precipitation on wet days (PRCPTOT), heavy precipitation (R10mm), and very heavy precipitation (R20mm) had a decreasing trend and change-point in western Iran.

The west of Iran is a mountainous region where most of the winter precipitation is supplied by the Mediterranean Sea system (Alijani and Harman, 1985; Ghalhari et al., 2016). Therefore, the decrease in annual precipitation in western Iran may be due to the poleward movement of the northern hemisphere storms under climate change conditions, which weakens the Mediterranean storm track and reduces the number of cyclones crossing the Mediterranean (Nissen et al., 2014). In this regard, Flocas et al. (2010) showed that the central frequency of Mediterranean cyclones is in January, and they decrease by August from the western Mediterranean to the east.

Also, precipitation in Iran is affected by other factors such as the El Niño-Southern Oscillation (ENSO) (Nazemosadat & Ghasemi, 2004), Southern Oscillation Index (SOI) (Roushangar et al., 2018), North Atlantic Oscillation (NAO) (Masih et al., 2011), Arabian anticyclone (Raziei et al., 2012), Red Sea Trough (Mofidi, 2005), and Asian summer monsoon (Babaeian & Rezazadeh, 2018). Changes in the Asian summer monsoon, to some extent, can determine the amount of precipitation in southeastern Iran.

Alizadeh and Choobari et al. (2016) showed that in the Lake Urmia basin, arable land has increased significantly in recent decades. Urmia is located in northwestern Iran. During the last four decades, CDD, CWD, R20mm, R30mm, R95pTOT, R99pTOT, and SDII indices showed an increasing trend. Daniels et al. (2015) also pointed out that urban land-use change is a factor in precipitation increase in the Lake Urmia basin. However, the spatial pattern of precipitation changes in Iran is complex and has different regional trends. Changes in Iran's precipitation result from the increasing intensity and are more important for changes in the average precipitation. A significant contribution to Iran's annual precipitation occurs in a few days of the year in the form of heavy and very heavy precipitation. In other words, the contribution of extreme indices in the annual precipitation in Iran has increased over the past four decades.