Investigating the Spatiotemporal Variation in Extreme Precipitation Indices in Iran from 1990 to 2020

Abstract

This study examines the spatiotemporal characteristics of extreme precipitation indices in Iran. It analyzes data from 38 synoptic stations across the country, covering the period from 1990 to 2020, focusing on the 11 most common extreme precipitation indices defined by the Expert Team on Climate Change Detection and Indices (ETCCDI). The analysis employs the Mann–Kendall (M–K) trend test. The findings indicate that the indices PRCPTOT (annual total precipitation), R20 mm (very heavy precipitation days), R10 mm (heavy precipitation days), R25 mm (number of wet days), Rx1 day (maximum 1-day precipitation), Rx5 day (maximum 5-day precipitation), SDII (simple daily intensity index), R95p (very wet day precipitation), R99p (extremely wet day precipitation), and CWDs (consecutive wet days) showed the highest values in the northern and western regions of the country, particularly at stations like Ramsar, Hamedan, Ilam, Kermanshah, and Yasouj. Conversely, the eastern and southeastern parts of the country showed the lowest values for these indices. The Consecutive Dry Day (CDD) index exhibited the highest values at Zabol station (228 days) and Abadan station (193 days) in the southern region of the country. Generally, precipitation extremes in the western, northwestern, and Caspian Sea coasts showed an increasing trend, while the eastern, southeastern, and central parts of the country demonstrated a decreasing trend. The trend test results indicate significant mutations in all precipitation indices, except for SDII, with mutation points primarily occurring during the decade from 2000 to 2010. The magnitude of mutation for each index post-mutation is generally greater than before. This study provides valuable information for decision-makers in agriculture, food security, water, and the environment. It also serves as a resource for natural disaster prevention and mitigation.

1. Introduction

Since the 1950s, human activities have driven climate change, impacting extreme weather and events across various regions of the Earth [1]. Global warming has resulted in significant challenges in the management of water and heat resources worldwide. Increasing temperatures have altered the timing and distribution of precipitation while also increasing the frequency and intensity of extreme climate events, such as droughts and floods, thereby exacerbating their effects [2]. The Expert Team on Climate Change Detection and Indices (ETCCDI) was established through a collaboration between the World Meteorological Organization (WMO), the World Climate Research Program (WCRP), and the Joint WMO/IOC Technical Commission for Oceanography and Marine Meteorology (JCOMM) to advance research on extreme climate conditions. They have defined 27 globally applicable indices that represent extreme climate events, including 11 for extreme precipitation and 16 for temperature extremes [3].

The frequent occurrence of extreme events usually causes numerous economic and social losses, especially in vulnerable countries. Therefore, investigating the characteristics of extreme climate events is very important [4]. In this regard, a comprehensive trend analysis was conducted to examine spatiotemporal changes in precipitation characteristics. The nonparametric Mann–Kendall test and quantile regression methods were used to identify possible temporal trends in 11 extreme rainfall indices used in this study. The results showed that most stations across Iran displayed drying trends, indicating a general reduction in annual precipitation in many regions of the country [5]. The authors of [6] conducted a study based on meteorological station data from the middle and lower reaches of the Yangtze River Basin (MLYRB) from 1970 to 2018, investigating the spatiotemporal distribution of 11 extreme precipitation indices and the correlation between large-scale atmospheric height and the calculated precipitation events. Their results showed that extreme precipitation indices mainly decreased in the northwestern MLYRB region at this spatial scale but increased along the eastern coastal region. The most abrupt variations in extreme indices were observed in the 1980s and 1990s.

In another study [7], the authors investigated trend changes in temperature and extreme precipitation indices using daily temperature and precipitation data from 76 synoptic stations across Iran from 1981 to 2010. They utilized the Mann–Kendall trend test and Sen’s slope to analyze the selected dataset. The findings for 11 temperature indices revealed that hot indices generally exhibited an increasing trend, whereas cold indices showed a decreasing trend. Regarding extreme precipitation indices, the results indicated a decline in both the amount and intensity of precipitation, along with an increase in the number of consecutive dry days. The authors of [8] studied Central Asia, analyzing data from weather stations and four precipitation datasets from 1950 to 2019. They utilized Taylor diagrams, geodetector, and other methods to investigate 10 extreme precipitation indices. Their study revealed a general increasing trend in extreme precipitation indices in Central Asia. An abrupt point occurred in 1986 when very wet day precipitation (R95p) increased. Additionally, their research demonstrated that abnormal increases in sea surface temperatures and other factors contributed to enhancing water vapor transport in Central Asia. This resulted from a sequence of storms and anticyclonic anomalies in the western region, leading to a surge in extreme precipitation events.

In [9], the authors investigated the spatiotemporal variation of extreme precipitation indices in the Chungcheong region of South Korea from 1973 to 2020. They analyzed 12 extreme precipitation climate indices derived from daily data collected at 10 synoptic stations. Utilizing the innovative trend analysis (ITA) method, they assessed trends in extreme precipitation characteristics related to duration, frequency, and intensity. The results indicated that most stations exhibited significant increasing trends in all investigated climate indices at a 95% confidence level, while only a few stations showed significant decreasing trends in R95p, R99p, Rx3day, and Rx5day. The authors of [10] examined the spatiotemporal trends of seven extreme precipitation indices in the Beijing River basin and along the south coast of China over the past 60 years. They analyzed daily precipitation data from 18 meteorological stations in China, covering the years 1959 to 2018. Their analysis utilized various statistical methods, including the Mann–Kendall trend test, the coefficient of variation, and continuous wavelet transformation. The M–K test results indicated significant changes in all seven precipitation indices, with notable mutation points occurring primarily during two periods: 1986–1991 and 2005–2010. Following these mutations, the magnitude of change for each index generally increased compared to the periods before the mutations. Additionally, the continuous wavelet transformation identified a significant oscillation period of 2–4 years for most indices across various time domains. Notably, the Consecutive Wet Day (CWD) index experienced a significant decrease.

In [11], the authors assessed the effects of warming trends on monsoon precipitation in Pakistan by analyzing eight precipitation indices over a 50-year period (1971–2020). They divided the data into two intervals: 1971–1998 and 1999–2020. Using Mann–Kendall and Sen’s methods, they evaluated both the direction and the magnitude of the observed trends. Their findings indicated that the most significant changes in precipitation extremes, characterized by increased intensity and frequency, occurred during the spring and summer monsoon in the second data period.

The authors of [12] conducted research using the usual methods of time series to investigate the changes in the main climate factors of temperature and precipitation in Bushehr during a statistical period of 50 years (1956–2005) and predict the future values for the climate factors. Their results showed that the most significant decrease in precipitation is related to 1973, the driest and least rainy year of the statistical period. Additionally, an increasing trend for temperature and a decreasing trend for precipitation are expected. The authors of [13] conducted a study to investigate whether the changes in precipitation and temperature trends in Iran are caused by climate change or natural climate variability. They analyzed these trends and their magnitude using quality-controlled daily data from 38 meteorological stations covering the period from 1966 to 2015. The analysis utilized the Mann–Kendall test and Sen’s slope method. The findings indicated that increasing temperatures are altering seasons, affecting their length and reducing the growing season for various plants. However, the Mann–Kendall test showed no significant trends in PRCPTOT, R10, R20, and R95p at most stations. Overall, there was an increase in temperature extremes and a decrease in precipitation indices.

Another study [14] examined extreme precipitation indices using daily precipitation data from 27 synoptic stations and 10 extreme precipitation indices from 1961 to 1990. Overall, their results showed all three states of stationary, upbeat, and negative trends in precipitation indices across Iran. Consistent with the Intergovernmental Panel on Climate Change (IPCC), this study has indicated the possibility of extreme precipitation, particularly in tropical regions. The results of this study all show the extraordinary complexity of the limiting behavior of precipitation patterns in Iran. In their research, the authors of [15] evaluated the variations in extreme precipitation indices using the daily data of the Global Precipitation Climatology Centre (GPCC) in the 1982–2016 period in Iran. Their results showed that the intensity of daily precipitation (SDII) is increasing in many parts of Iran. Also, in many areas of Iran, especially in the western parts, the Consecutive Wet Day (CWD) index is decreasing.

According to a comprehensive review of research on climate change, its significant impacts on extreme weather events are highlighted, particularly in vulnerable countries like Iran. However, there are few studies examining changes in extreme precipitation in Iran based on data from the past two decades. Given the diverse behaviors and complex processes of extreme precipitation across different regions, as well as the varying trends in climate extreme indices, further investigation into precipitation indices is essential, particularly in countries with diverse climate zones like Iran. This study aims to analyze the spatiotemporal characteristics of 11 extreme precipitation indices in Iran, assess their variations, and identify significant change points in their time series, which indicate the onset of extreme events.

This study is organized as follows: Section 2 outlines the study area, the meteorological stations utilized, and the data analysis methods employed; Section 3 provides the results and discussion; and finally, Section 4 concludes the study and suggests directions for future research.

2. Materials and Methods

2.1. Study Area

Meteorological Stations and Quality Check of Data Iran, located in Southwest Asia, is a high plateau spanning 1,648,195 km² between 25° and 40° N latitudes and 44° and 64° E longitudes (Figure 1). It shares borders with the Caspian Sea to the north and the Oman Sea and the Persian Gulf to the south. The country experiences diverse climates from north to south due to its wide range of latitudes and longitudes, resulting in four distinct seasons. While cities along the northern coast have a humid climate, the southern coastal areas have a dry climate, facing water scarcity, frequent droughts, and reliance on groundwater resources [16]. Annual precipitation in most regions ranges from about 350 mm to less than 50 mm [17]. For this study, we identified synoptic stations nationwide with long-term daily precipitation data records. After ensuring data quality, we finally selected 38 meteorological stations with reliable long-term data from 1990 to 2020, provided by the Islamic Republic of Iran Meteorological Organization (IRIMO). The locations of these stations are shown in Figure 1. Homogeneity testing is essential in climatological research, particularly when assessing climate change [18]. Long-term climate data from weather stations can be affected by non-climatic factors, including changes in instruments, observers, site locations, or surrounding environments [19]. In this study, we used the RHtests/V4 dlyPrcp software in R to assess the homogeneity of precipitation data. This software detects and corrects artificial shifts in climate data series that are not related to climate change (https://github.com/ECCC-CDAS/RHtests, accessed on 1 March 2019). The results of the RH tests showed no significant inhomogeneities that required mean adjustments. Therefore, we used the original data series to compute extreme precipitation indices according to the ETCCDI definitions [3], based on the daily precipitation data (

Table 1. Information for precipitation extreme indices used in this study, defined by the ETCCDI.

Index	Index Name	Definition	Unit
R10 mm	Heavy precipitation days	Annual count of days when RR ≥ 10 mm	day
R25 mm	Number of wet days	Annual count of days when RR ≥ 25 mm	day
R20 mm	Very heavy precipitation days	Annual count of days when RR ≥ 20 mm	day
CDD	Consecutive dry days	Maximum number of consecutive days with RR< 1 mm	day
CWD	Consecutive wet days	Maximum number of consecutive days with RR≥ 1 mm	day
SDII	Simple daily intensity index	Annual total precipitation divided by the number of wet days in the year	mm/day
R99p	Extremely wet day precipitation	Annual total precipitation when RR > 99p	mm
Rx1 day	Maximum 1-day precipitation	Monthly maximum 1-day precipitation	mm
Rx5 day	Maximum 5-day precipitation	Monthly maximum 5-day precipitation	mm
PRCPTOT	Annual total precipitation	Annual total precipitation on wet days (RR ≥ 1)	mm
R95p	Very wet day precipitation	Annual total precipitation when RR > 95p	mm

).

2.2. Data Processing Method

2.2.1. Mann–Kendall (MK) Trend Test

In this study, we employed the Mann–Kendall trend test (MK test) [20,21,22] to detect significant trends in selected climate variable time series. The MK test is a nonparametric method that does not assume linearity or normal distribution in the data. Additionally, it is capable of identifying monotonic upward or downward trends. As defined in Ref. [23], the MK statistic (S) is calculated as follows:

$$\mathrm{S}={\sum }_{\mathrm{i}=1}^{\mathrm{n}-1}{\sum }_{\mathrm{j}=\mathrm{i}+1}^{\mathrm{n}}\mathrm{s}\mathrm{g}\mathrm{n}\left({\mathrm{x}}_{\mathrm{j}}{\mathrm{x}}_{\mathrm{i}}\right)$$

(1)

$$\mathrm{s}\mathrm{g}\mathrm{n}\left({\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{i}}\right)=\left\{\begin{array}{c}+1 \mathrm{i}\mathrm{f}({\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{i}})>0\\ 0 \mathrm{i}\mathrm{f}\left({\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{i}}\right)=0\\ -1 \mathrm{i}\mathrm{f}\left({\mathrm{x}}_{\mathrm{j}}-{\mathrm{x}}_{\mathrm{i}}\right)<0\end{array}\right.$$

(2)

where xj and xi are the jth and ith terms, respectively, in a time series of size n. Equation (2) calculates the number of positive differences minus the number of negative differences. Therefore, a positive S indicates that the most recent data are larger than the previous data, suggesting an upward trend, while a negative S indicates the opposite. For n ≥ 10, the average E and variance (Var) of S are given in Equations (3) and (4).

$$\mathrm{E}\left(\mathrm{S}\right)=0$$

(3)

where the mean is 0 since the authors of [24] already proved that S is asymptotically and normally distributed for time series with n ≥ 10.

$$\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)={\displaystyle \frac{1}{18}}\left[\mathrm{n}\left(\mathrm{n}-1\right)\left(2\mathrm{n}+5\right)-{\sum }_{\mathrm{i}=1}^1{\mathrm{t}}_{\mathrm{i}}\left({\mathrm{t}}_{\mathrm{i}}-1\right)({2\mathrm{t}}_{\mathrm{i}}+5)\right]$$

(4)

where t is the number of tied groups in the time series, and t_i is the volume of data in the ith tied group. The statistics of the standard test (Z) can be calculated as follows:

$$\mathrm{Z}=\left\{\begin{array}{c}{\displaystyle \frac{\mathrm{S}-1}{\sqrt{\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)}}}\mathrm{i}\mathrm{f} S>0\\ 0 \mathrm{i}\mathrm{f} S=0\\ {\displaystyle \frac{\mathrm{S}+1}{\sqrt{\mathrm{V}\mathrm{a}\mathrm{r}\left(\mathrm{S}\right)}}}if S<0\end{array}\right.$$

(5)

In the Mann–Kendall trend test, Z is used to assess the significance of the trend by testing the null hypothesis (H0), which posits that there is no monotonic trend in the data. The alternative hypothesis (Ha) implies that a trend does exist in the time series.

If $\left|Z\right|$> Z_1-${\displaystyle \raisebox{1ex}{$\alpha $}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$, H0 is rejected, and Ha is accepted, indicating that the trend is significant at the chosen significance level (α). For a two-tailed test, the Z values corresponding to significance levels of 5% and 10% are critical thresholds. For instance, if the value of Z falls within the range that does not exceed the critical threshold, we accept H0, suggesting that the trend is non-significant. Conversely, if $\left|Z\right|$> 1.96, we reject H0, indicating that the trend is significant at α = 0.05. A positive Z value indicates an upward trend, while a negative Z value signifies a downward trend.

2.2.2. Sen’s Slope Estimator

The SS estimator calculates the trend magnitude in the chosen indices [11]. Sen’s formula calculates the variation within the selected data series based on the slope value. This variation over time is estimated relative to the mean daily discharge. Relative units are used because there is significant variation in discharge between the two gauges, making it challenging to compare absolute changes. Comparing the changes in daily discharge becomes difficult due to the small magnitude of change. In the first phase, N pairs of data were computed using the following relation:

$$\mathrm{Q}={\displaystyle \frac{x_j-x_k}{j-k}}if j>k$$

(6)

Sen’s estimator of slope calculates the median of N values of Q. To obtain the median of the N slopes, the N values of Qi are arranged in ascending order. The formula for Sen’s estimator is as follows:

$Se{n}^{\mathrm{\prime }}s Estimator=Q\left[{\displaystyle \raisebox{1ex}{$\left(N+1\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right]$ If N was odd,

$${\displaystyle \frac{1}{2}}\left(\mathrm{Q}{\displaystyle \frac{\mathrm{N}}{2}}+\mathrm{Q}{\displaystyle \frac{\left(\mathrm{N}+2\right)}{2}}\right)$$

(7)

In the end, Qmed uses a double-tailed test with a 100 (1 − α)% confidence interval, while Sen’s method allows for a true slope.

2.2.3. Detection of Mann–Kendall Mutation

According to [10], we used the Sequential Mann–Kendall (S-MK) test to determine whether a series is increasing or decreasing over time. This test provides graphical results and can also identify the starting point of the trend [24]. In this test, the time series ($D_2‚ D_3‚\dots ‚ \mathrm{a}\mathrm{n}\mathrm{d} D_n)$ creates an organized column $r_i$, which represents the accumulated sample number of $D_i>D_j\left(1\le j\le i\right).$ The rank series $\left(S_k\right)$ is calculated as follows:

$${\mathrm{S}}_{\mathrm{k}}={\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{r}}_{\mathrm{i}}(\mathrm{k}=2\mathrm{‚}3\mathrm{‚}\dots \mathrm{‚}\mathrm{n})$$

(8)

When D_i > D_j, r_i = 1; when D_i _ D_j, ri = 0 (j = 1, 2, …, i). The expected value E(S_k) of S_k and its sequence variance Var (S_k) are calculated as follows:

$$\mathrm{E}\left({\mathrm{S}}_{\mathrm{k}}\right)=\mathrm{n}(\mathrm{n}+1)/4$$

(9)

$$\mathrm{V}\mathrm{a}\mathrm{r}\left({\mathrm{S}}_{\mathrm{k}}\right)=\mathrm{n}\left(\mathrm{n}-1\right)(2\mathrm{n}+5)/72$$

(10)

The data sequence is considered independent, and the test statistic (UF_k) is calculated as follows:

$${\mathrm{U}\mathrm{F}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{S}}_{\mathrm{k}}-\mathrm{E}\left({\mathrm{S}}_{\mathrm{k}}\right)}{\sqrt{\mathrm{V}\mathrm{a}\mathrm{r}\left({\mathrm{S}}_{\mathrm{k}}\right)}}}\left(\mathrm{k}=1\mathrm{‚}2\mathrm{‚}\dots \mathrm{‚}\mathrm{n}\right)$$

(11)

UFk follows a standard normal distribution and represents a significance level, denoted by a. The critical value U$\alpha$ can be obtained from the standard normal distribution table. For instance, if a is set to 0.05, we can determine the corresponding critical value U. $\pm 1.96$. If |UF_k| > |U$\alpha$|, it indicates a significant increasing or decreasing trend in the time series. We plotted the UF_k points for the study period as a curve to analyze whether there was a decreasing or increasing trend. Then, we repeated the steps in reverse order. We multiplied the resulting value by −1 to obtain a new time series, called UB_k. We drew sequence diagrams for both (UF_k or forward) and (UB_k or reverse). If UF_k > 0 or UF_k < 0, it means there is an increasing or decreasing trend, respectively. When UF_k exceeds the critical value, the increasing or decreasing trend becomes statistically significant. The intersection point between the UF_k and UB_k curves indicates the start of a mutation [25,26].

The data analyses were conducted using R 4.3.2 software. The maps were created using ArcGIS 10.7.1 (ESRI Inc., Redlands, CA, USA). To interpolate the spatial distribution of precipitation indices, the IDW interpolation method was applied, based on the studies by [27,28].

3. Results and Discussion

3.1. Spatial Variation in Extreme Precipitation Indices

Figure 2 shows the spatial variations in 11 extreme precipitation indices in Iran. According to this figure, the PRCPTOT index varies between 48.77 and 1238.59 mm. The lowest values of this index are related to the eastern and southeastern regions, such as Yazd, Kerman, Birjand, and Zahedan provinces. In contrast, the highest values are related to the northern part of the country and a number of western provinces, such as Ilam and Hamedan. Ramsar station has the highest values among all the study stations, and Yazd station has the lowest values of this index. The R25 index (very heavy precipitation days) varies between 1 and 13 days. According to the results of this index, except for a few northern stations of the country, including Ramsar and Amol, as well as Yasouj in the southwest, the number of events with very heavy rainfall is very low. The maximum 1-day precipitation (Rx1 day) varies between 12.2 and 153 mm. Its lowest values are related to the eastern half of the country, especially Yazd, Sistan, and Baluchistan provinces, and the highest values are related to the northern part of the country, the west, and the southwest. Among all the study stations, Ramsar, Yasouj, and Ilam recorded the highest Rx1 day. The maximum 5-day precipitation index (Rx5 day) has values between 181 and 230 mm across the country, with the highest values related to the northern and Yasouj provinces in the southwest of Iran, and the eastern half has the lowest values of this index.

The Simple Daily Intensity Index (SDII) ranges from 4 to 15.96 mm per day. Most regions of the country exhibit the lowest values for this index, with the exception of the southern regions and parts of the provinces bordering the Caspian Sea. The indices for very wet days (R95p) and extremely wet days (R99p) show similar trends at the national level, being highest in the western and northern parts of the country, while the eastern provinces report the lowest values. The Consecutive Dry Day (CDD) index varies from 33 to 229 days. Results indicate that the southern half of the country has experienced the driest conditions, recording less than one millimeter of rain. Notably, the Zabol station has the highest number of consecutive dry days at 228, followed by Abadan with 193 consecutive dry days. Conversely, the northern half of the country experiences fewer consecutive dry days, particularly as one approaches the Caspian Sea border. The Consecutive Wet Day (CWD) index ranges from 3 to 6 days, with the lowest values found in southeastern Iran, while the highest counts of wet days are observed in the western, northwestern, and northern regions. The indices for heavy precipitation days (R10 mm) and very heavy precipitation days (R20 mm) in the eastern and southeastern parts of the country show negligible values. Overall, the spatial distribution of extreme precipitation indices in Iran indicates that the highest values for indices such as PRCPTOT, R20 mm, R10 mm, R25 mm, Rx1 day, Rx5 day, SDII, R95p, R99p, and CWD are predominantly found in the northern and western regions. In contrast, the CDD index shows the highest values in the southern half, especially in southeastern areas like the Zabol station. The highest values for two additional indices are associated with provinces in the western and northern parts of the country, particularly at the Ramsar station.

These findings align with previous research, such as that of [29], which indicated that the coastal areas of the Caspian Sea and the western regions experience the highest occurrences of heavy and super heavy rainfall. Similarly, [30] found that the Caspian coast and northwest regions of the country have the highest frequency and average rainfall.

3.2. Analysis of Trend Change and Mutation Point

In the study’s next step, linear trends of extreme precipitation indices and sequence Mann–Kendall statistics graphs of the indices during the statistical period under review (1990–2020) were drawn (Figure 3 and Figure 4). According to the two figures, the two indices of maximum 1-day precipitation (Rx1 day) and maximum 5-day precipitation (Rx5 day) have the same variations. There is a mutation in the data series of the maximum precipitation index for 1999, and an increasing trend is observed for 4 years; after that, again for 2003, there is a mutation in the data series. Until the end of the period, the 1-day maximum precipitation index has a downward trend. The maximum 5-day precipitation index (Rx5 day) also has a decreasing trend; no mutation is observed in this data series. They decrease with an almost uniform slope. The R95p index generally has a decreasing trend until the end of the period, but two mutations occur in the 2001 and 2003 time points. A decreasing trend of this index is observed from the beginning of the period until 2001, when a mutation occurs in the data. However, there is an increasing trend for two consecutive years from 2001 to 2003, and after that, until the end of the period, there is a decreasing trend of the index.

The R99p index generally has a decreasing trend until the end of the period, but in the time series of this index, there are two mutations, one related to 1999 and the other in 2003. After both mutations, the data exhibit an increasing trend, followed by a decrease until the end of the period in the data series. The time series of the PRCPTOT index has a decreasing trend in the entire statistical period, except for the 2019 time point, when the value of this index increases. Two mutations occur in its time series, and the interval between them exhibits a slightly upward trend in the index. After the second mutation in the data, this index exhibits a decreasing trend until the end of the period.

The time series of the SDII has many variations. The values of this index show a downward trend from the beginning of the period until 1998, followed by an upward trend from 1998 to 2004, and another downward trend until the end of the period. This trend is also evident in the index’s forward and reverse time series. Furthermore, there are no mutations in the time series of this index. In contrast, the time series of three other indices, namely R10, R20, and R25, demonstrate a consistent downward trend throughout the entire period. This downward trend is also evident in all three indices’ forward and reverse trends. In the case of R10 and R20, two mutations occur in their time series for the 2001 and 2003 time points. Between these two mutations, the data series shows an increase followed by a decrease until the end of the period. Lastly, both the CDD and CWD indices exhibit a decreasing trend until the end of the period. The time series of both forward and reverse precipitation data, like the extreme precipitation indices, exhibits a decreasing trend until the end of the period. Notably, between 2000 and 2010, there were two significant mutations in the time series. After each mutation, the subsequent decreasing trend was steeper than the previous one.

By analyzing the extreme precipitation indices and precipitation data graphs for the period under review, it is evident that the precipitation data in this period also show a decreasing trend. As we approach the period’s end, the decrease in precipitation becomes more significant. Additionally, two distinct mutations in the data are observed during the 2000–2010 decade. When comparing the results of this research with previous studies, such as [6,7,10], it should be emphasized that these previous studies similarly reported that extreme precipitation indices exhibit a decreasing trend, and there is a mutation in the time series of these indices. Thus, our results show good agreement, as we also found that the trend after the mutation is more significant.

3.3. Analysis of Spatial Variation in the Trend of Extreme Precipitation Indices

According to Figure 5, which shows the spatial variations in extreme precipitation index trends in Iran, the R10 mm index decreases in most regions of the country, except for parts of the north and northwest, during the statistical period under review. In particular, a decreasing trend can be observed in the southern and eastern half of the country. The PRCPTOT index also decreases in most regions, except for the north and northwest parts. The R20 mm index exhibits varying trends in the country, increasing in some areas and decreasing in others. The SDII shows an increasing trend in most regions of the country (21 stations out of 38 stations). These results are consistent with the findings of [6,7,10,13]. The Rx5 day index shows a decreasing trend in the country’s southern half and an increasing trend in the western, northwestern, and northern parts. Similarly, Rx1 day, like Rx5 day, decreases in the country’s southern half and increases in the western and northeastern parts. The R95p and R99p indices indicate a decreasing trend in the southern half and an increasing trend in the country’s northern half.

The CWD index exhibits a decreasing trend in most study stations, consistent with the research findings of [10,13,14]. The R25 mm index also decreases in the southern half and increases in the northern half, particularly in the west, north, and northwest. An analysis of 11 extreme precipitation indices reveals a decreasing trend in the southern provinces and an increasing trend in the northern regions, especially in the west and northwest of the country. It is important to note that the significance level for evaluating these indices was 5%. Notably, the PRCPTOT index in Zabol station exhibits a significant decreasing trend at a 5% significance level, while the R10 index in Bushehr station shows a decreasing trend. Zabol station also displays a significant negative trend for R20, while Kermanshah station shows a significant increasing trend for R25. Zabol station has a significant decreasing trend for R95p, whereas a significant decreasing trend is observed for R99p in Zabol station, and a significant increasing trend is observed in Ilam.

Additionally, Ilam station has a significant increasing trend for Rx1 day, while Orumiye station displayed a significant increasing trend for Rx5 day, with significant decreasing trends in Bushehr and Birjand stations. Generally, the extreme precipitation indices in the Alborz and Zagros regions and along the Caspian Sea coasts show an increasing trend. On the other hand, these indices exhibit a decreasing trend in the southwestern, southeastern, and central parts of Iran.

In addition to calculating Mann–Kendall’s trend test at the study stations, Sen’s slope trend magnitude test was also calculated, as indicated in

Table 2. Sen’s slope trend in extreme precipitation indices during the study period.

Station	CDD	CWD	R10 mm	R20 mm	R25 mm	SDII	Rx5 Day	Rx1 Day	PRCPTOT	R95p	R99p
Abadan	−0.16	0.00	−0.07	0.00	0.00	0.00	−0.20	−0.33	−2.29	−1.73	−0.43
Abali	−0.42	0.05	0.28	0.05	0.00	0.03	0.30	0.11	4.69	2.25	0.79
Ahvaz	0.70	0.00	−0.09	0.00	0.00	0.03	−0.45	0.15	−2.10	−1.15	0.10
Amol	0.66	0.00	0.09	0.22	0.00	0.04	2.06	0.25	4.92	2.63	−0.11
Arak	0.13	0.00	0.00	0.00	0.00	0.02	0.30	0.25	0.98	0.98	0.64
Avaj	0.17	0.00	−0.09	0.00	0.00	−0.02	−0.43	−0.33	−0.31	−0.74	−0.41
Babolsar	0.27	0.00	0.00	0.00	0.00	0.04	0.17	0.27	−1.20	−0.53	0.49
Bandarabbas	0.50	0.00	−0.06	0.00	0.00	−0.04	−1.17	−0.69	−2.67	−2.41	−1.61
Baneh	0.91	0.08	0.40	0.18	0.11	0.02	1.33	1.00	9.71	4.68	2.04
Birjand	−0.24	0.00	0.00	0.00	0.00	0.01	−0.56	−0.24	−2.15	−1.39	−0.50
Bojnurd	−0.80	0.00	0.00	0.00	0.00	0.01	0.26	0.08	−0.84	−0.44	0.21
Bushehr (Airport)	0.00	0.00	−0.04	0.00	0.00	0.04	0.52	−0.38	−0.72	−0.22	−0.27
Firuzkuh	−0.07	0.00	0.00	0.00	0.00	0.02	0.00	0.28	0.83	0.98	0.28
Gorgan	0.36	0.00	−0.09	0.00	0.00	0.02	−0.27	0.16	−2.05	−1.00	0.18
Hamedan	0.80	0.00	0.06	0.00	0.05	0.05	0.50	0.33	0.90	1.53	0.97
Ilam	−0.75	0.00	−0.18	−0.05	0.00	0.00	0.56	−0.12	−3.73	−0.82	−0.38
Karaj	−0.82	0.00	0.05	0.00	0.00	−0.02	0.10	−0.08	1.39	0.43	0.18
Kerman	0.31	−0.05	0.00	0.00	0.00	0.02	−0.01	−0.11	−1.33	−0.78	−0.50
Kermanshah	0.52	0.00	−0.06	0.00	0.00	0.06	0.79	0.55	0.00	0.99	1.53
Khorramabad	−0.18	0.00	−0.11	0.00	0.00	0.02	0.25	0.48	0.63	0.91	0.96
Khoy	−0.43	0.00	0.08	0.00	0.00	0.01	0.36	0.35	2.24	1.19	0.75
Mashhad	0.11	0.00	0.00	0.00	0.00	0.02	0.07	0.21	0.26	0.60	0.48
Orumiye	0.17	0.00	0.00	0.00	0.00	0.00	−0.33	−0.20	1.26	0.31	0.10
Qazvin	0.17	0.00	0.00	0.00	0.00	−0.01	−0.02	0.00	−0.68	0.00	−0.37
Ramsar	0.41	0.00	0.13	0.11	0.08	0.07	−0.81	−0.28	5.12	4.17	0.84
Sanandaj	0.08	0.00	0.00	0.00	0.00	−0.01	−0.29	0.00	−3.13	−0.90	−0.08
Sari	0.55	0.00	0.12	0.00	0.08	0.05	0.36	0.45	4.27	3.74	3.43
Saveh	−1.16	0.00	0.00	0.00	0.00	−0.01	0.28	0.00	−0.54	−0.30	−0.26
Semnan	0.00	0.00	0.00	0.00	0.00	−0.01	−0.20	0.11	−0.08	−0.09	0.12
Shahrekord	−0.13	0.00	0.00	−0.05	0.00	−0.01	−0.66	−0.21	−1.22	−1.29	−0.70
Shiraz	−0.37	−0.06	−0.17	−0.06	0.00	−0.04	−1.45	0.17	−3.97	−1.77	0.00
Tabriz	−0.14	0.00	0.00	0.00	0.00	0.02	0.40	0.16	2.64	1.22	0.69
Tehran (Airport)	−0.08	0.00	0.00	0.00	0.00	−0.01	−0.37	−0.16	0.70	0.29	−0.28
Yasouj	−0.72	0.00	−0.25	−0.14	−0.07	0.00	−1.14	−0.30	−5.55	−1.69	−1.09
Yazd	0.40	0.00	0.00	0.00	0.00	−0.03	−0.16	−0.06	−0.50	−0.41	−0.29
Zabol	−1.25	0.00	0.00	0.00	0.00	−0.05	−0.30	−0.25	−1.84	−1.73	−0.77
Zahedan	1.00	0.00	0.00	0.00	0.00	0.00	−0.22	−0.07	−0.58	−0.45	−0.10
Zanjan	0.22	0.00	0.00	0.00	0.00	0.02	−0.02	−0.16	0.96	0.80	−0.48

Note: Bold numbers in the table indicate significance at the 5% level.

. The results show that two indices, CDD and SDII, exhibit an increasing trend in most of the country’s stations (23 out of 38 stations for CDD and 27 out of 38 stations for SDII). The increasing trend in the CDD index is statistically significant at the 0.05 level for three stations: Ramsar, Zabol, and Gorgan. On the other hand, Rx1 day, Rx5 day, PRCPTOT, R95p, and R99p demonstrate a decreasing trend in most of the country’s stations. The most pronounced decreasing slope is observed in the PRCPTOT index, which is statistically significant in the Birjand and Zabol stations. R10, R20, and R25 mm show a decreasing trend in some stations, while no significant trend is observed in the majority of the study stations.

The findings of this study align with those of previous researchers, such as [31], who reported a decreasing trend in precipitation indices in the central, eastern, and southeastern regions of Iran, and [14], who found a decreasing trend in precipitation indices across most stations in Iran. Additionally, [7] reported a decreasing trend in precipitation indices nationwide, except for the CDD index and SDII.

4. Conclusions

Due to climate change and its significant impact on extreme weather events, increasing attention has been paid to extreme precipitation in regions influenced by climate change and human activities. This study investigated the spatiotemporal trends of extreme precipitation indices in Iran from 1990 to 2020, using daily precipitation data from 38 synoptic stations. The key findings of this research are as follows:

Spatial variations in the annual average of 11 extreme precipitation indices, namely PRCPTOT, SDII, Rx1 day, Rx5 day, CDD, R10 mm, R20 mm, R25, R95p, R99P, and CWD, were similar. The highest values of these precipitation indices, except for the CDD index, were observed in Iran’s northern and western regions. In contrast, the lowest values were found in the eastern and southeastern parts of the country. The CDD index showed the highest values in southern Iran and the lowest values in northern and western stations. The R95p and R99p indices displayed similar variations, with higher values in the western and northern regions and lower values in the eastern provinces. The R10 mm and R20 mm indices had insignificant values in the east and southeast, with higher values in the west and north, particularly at the Ramsar station. Generally, among all study stations, Ramsar station recorded the highest values, while Yazd and Zabol stations had the lowest values for these indices, except for CDD.

The Mann–Kendall test revealed that stations in Iran’s southern, southeastern, eastern, and central plateau regions demonstrated a decreasing trend. In contrast, stations located in the Alborz and Zagros regions and along the coasts of the Caspian Sea exhibited increasing trends. The CWD index significantly decreased across many stations, while the SDII increased in most regions. The CDD index showed an increasing trend across the country, particularly in the southern and eastern regions. The Mann–Kendall statistics data showed a mutation in the time series of the indices, indicating a mutation in the occurrence of extreme events. This mutation was observed twice in the time series, spanning three years between 2000 and 2010, across all stations. For all indices, there was a decreasing trend until the end of the period, so the increasing trend after the mutation was more significant than the trend before the mutation.

This study shows that the geographical attributes of different regions influence changes in extreme precipitation indices. Specifically, the western, northwestern, and Caspian Sea coasts demonstrate an increasing trend, while the country’s eastern, southeastern, and central parts exhibit a downward trend. However, these trends are not significant in the majority of the stations. Consequently, forthcoming studies about extreme precipitation indices necessitate a regional division based on geographical and climatic characteristics. Furthermore, it is crucial to augment the number of study stations, particularly in the eastern and central regions of Iran, to identify mutation points as the starting point of extreme events in the time series of extreme precipitation indices and to enhance our comprehension of extreme weather conditions.