Spatiotemporal analysis of precipitation variability based on entropy over Iran

Precipitation is one of the most variable climatic elements, exhibiting plenty of temporal and spatial variations. There is significant variation in precipitation, especially in regions with lower amounts. With a mean annual precipitation of about 250 mm, Iran is considered an arid country, as the global average is 960 mm. Although Iranians have long adapted to low precipitation and its fluctuations, any change in the amount or distribution of precipitation will transform life in the country (Masoudian 2011). Precipitation, as a climatic element and process, is highly sensitive to climatic changes. Any fundamental change in the amount, type, and pattern of precipitation can have significant consequences (Tegart et al. 1990), affecting other elements of climate as well as biological, economic, and social activities in a feedback loop. Therefore, it is of great importance to understand variability in precipitation due to its significance in a large number of areas, including natural areas (as in the hydrologic cycle or the general circulation of the atmosphere) and economic areas (as in agriculture, industry, or services) (Marengo et al. 2001). In this research, the H-Index and the D-Index are used to identify spatiotemporal changes in precipitation and analyze water resources over Iran. Applying the theory of entropy in studies can contribute to better analysis and understanding of the variability in the spatial patterns of the phenomena being analyzed (Silva et al. 2017).

Masoudian (2006) analyzed the water resource regions over Iran using the index of precipitation entropy from 1951 to 1999 and statistical analysis methods for data analysis. Also, the index measures the uncertainty in the annual share of precipitation. The research results demonstrated that the H-Index could express the characteristics of precipitation in the country. The H-Index was combined with the annual precipitation of Iran to enable the zoning of the country in terms of the potential availability of water resources, and it was found that there were four water resource availability regions in Iran. Zamani et al. (2018) investigated the daily, seasonal, and annual behavior of precipitation concentration in Jharkhand State on the Indian Peninsula. According to their results, plenty of irregularity and inconsistency was observed in different parts of the region due to heavy daily precipitation. Simultaneously, there was an incremental trend in annual precipitation in the east and northeast, which reduced values for the precipitation concentration index. Unlike during the peak precipitation season (summer), there was an incremental trend in winter for precipitation concentration. Roushangar & Alizadeh (2018) investigated annual precipitation change detection in Iran using the function decomposition method. According to their results, precipitation entropy decreased as latitude dropped in the south, exhibiting a decreasing trend. They also found a close relationship between longitude and mean annual entropy in Iran. In his analysis of the trend and homogeneity of precipitation in Iran, Javari (2016) stated that there was great diversity in seasonal precipitation patterns in Iran, and less spatial coherence was observed concerning the temporal patterns in seasonal precipitation. He also suggested that the variation in seasonal precipitation exhibited a decreasing trend in the central and eastern regions and an incremental trend in the west and north. Investigating a different issue within the area of Iran, Mohammadi & Sancholi (2013) found in their analysis of the precipitation concentration index variation in the semi-arid regions that the entire study area exhibited significant intra-annual variation, indicating the seasonal quality of precipitation in the arid regions of Iran. They also suggested that the increase in the seasonal rate and precipitation concentration in different parts has led to increased irregularity and fluctuation in the area.

In their analysis of precipitation over Saudi Arabia, Hasanean & Almazroui (2015) divided the statistical period into two periods. The first period showed slight fluctuation and an incremental trend from 1978 to 1993 (12.5 mm per decade), while the second period showed more significant precipitation fluctuation and a decreasing trend from 1993 to 2009 (35.1 mm per decade). These variations in precipitation played substantial roles in subtropical jet streams with two patterns: the Southern Oscillation Index and the North Atlantic Oscillation. In their analysis of the trends in heavy precipitation indices over Iran, Balling et al. (2016) analyzed trends in heavy precipitation indices over Iran and found an incremental trend across the country, with a significant trend observed from southwest to northeast. They also observed that this significant trend occurred particularly in the western and northern parts of Iran during the statistical period from 1950 to 2007, and the more significant occurrence in the cold seasons and the reduction in the others have caused the precipitation to concentrate over the country. Various regions worldwide have experienced this precipitation variation, such as China. Ma et al. (2015) found that precipitation intensity has changed over the past six decades, shifting from very low and mild to heavy and ultra-heavy. The frequency of floods and consecutive dry days has significantly increased, while the frequency of rainy days has decreased in most regions of China. Gallego et al. (2006) analyzed the variation in the frequency and intensity of daily precipitation over the Iberian Peninsula in Spain. According to the results, mean precipitation and the frequency of moderate to heavy precipitation have decreased during the past few decades, while the frequency of days with low to mild precipitation has undergone an incremental trend. An entropy analysis was made by Mishra et al. (2009) based on the variation in precipitation over Texas, United States. It was found that the frequency of rainy days and precipitation have gradually decreased during the statistical period from 1900 to 2005, and precipitation entropy has increased over Texas as a consequence. The trends in pervasive and persistent drought over the entire state were incremental in the 1950s and from 1990 to 2006. Nazaripour & Mansouri Daneshvar (2014) investigated the spatial variation in 1-day precipitation in Iran. On that basis, precipitation in Iran had durations of 1–45 days, where 1-day precipitation has experienced a decreasing trend of 17.5% all over Iran. This has reduced mean precipitation and the total frequency of rainy days over a large part of the arid regions in the eastern and central half of the country, given the high frequency of such days concerning the total frequency of rainy days over that part of Iran. In a study of the variation in heavy and mean precipitation in Iran, Rahimi & Fatemi (2019) demonstrated that there has been a decreasing trend in annual precipitation during the period from 1960 to 2017 at most stations around the country. Heavy precipitation, rainy days, and severe wet periods have been restricted to the Caspian coasts in the north and the southern coasts. A review of research conducted both within Iran and the world reveals that most studies focus on variations in precipitation trends at different intensity levels. Therefore, this study aims to provide a more reliable and accurate assessment of the temporal entropy of precipitation and identify water resource regions in Iran by utilizing long-term, high spatial density versions of precipitation data.

The daily gridded precipitation data from the Asfazari database were utilized for this research. The database has been interpolated over Iran using the geostatistical method of Kriging. With a spatial resolution of 0.25° × 0.25° (2,491 grids), this precipitation database was created in 20,819 days, from 01/01/1962 to 31/12/2019.

The nonparametric Mann–Kendall test was first presented by Mann (1945) and then extended by Kendall in 1948 (Kendall 1975). It can fit onto a non-normal time series that follows no particular distribution. This method is used to test the hypothesis that the sequence of data is random as opposed to the existence of a trend. In the current study, the modified nonparametric Mann–Kendall test was used to eliminate the impact of autocorrelation on trend detection (Hamed & Rao 1998). Sen's slope estimator was used to estimate the change rate. The World Meteorological Organization (WMO) has recommended two statistical methods, such as the Mann–Kendall test and Sen's slope estimator application.

Water resource regions are defined based on the coupled H-Index and annual precipitation over the study area, as follows:

Abundant and permanent: It consists of regions with mean annual precipitation values greater than the country's long-term mean precipitation and an insignificant seasonal pattern (the H-Index greater than the mean value over the country).

Deficient and permanent: It consists of regions with mean annual precipitation values less than the country's long-term mean precipitation and an insignificant seasonal pattern (the H-Index greater than the mean value over the country).

Deficient and concentrate: It consists of regions with mean annual precipitation values less than the country's long-term mean precipitation and a significant seasonal pattern (the H-Index less than the mean value over the country).

Abundant and concentrate: It consists of regions with mean annual precipitation values greater than the country's long-term mean precipitation and a significant seasonal pattern (the H-Index less than the mean value over the country).

All the statistical calculation and programming is done in the MATLAB environment.

According to Figure 6(a), during the statistical period of 57 years, the abundant and permanent water resource region in Iran was located in the northern half of the country along the Zagros Mountains in the west and Alborz Mountains in the north.

The water resource region with deficient and permanent precipitation is found in the southern part of the Alborz Mountains and the eastern part of the Central Zagros Mountains, extending longitudinally up to the northeastern borders.

The country's most extensive water resource region has experienced deficient and concentrate precipitation, covering large parts of the south, center, and east.

Finally, the least vast water resource region is located in southwest Iran and consists of the southern part of the Zagros Mountains.

The considerable sudden change observed in 1998 in the values of the H-Index and precipitation parameters caused the long-term period under examination to be divided into two periods: one before that year's sudden change and the other after that. This division allowed for a comparison of the variability in water resource regions between the two periods. The comparison of areas before and after the sudden change (Figure 6(b) and 6(c)) indicates a significant difference in their sizes. The permanent water resource regions with abundant and deficient precipitation and also abundant and concentrate regions experienced a reduction after 1998. In contrast, the region with deficient and concentrate precipitation has extended over a larger region from 46.01% to more than 50.54% of Iran's total area. The most severe reduction was observed in the abundant and permanent water resource region, with a decrease of 2.97% (equivalent to 48,957.04 km²) in the country's northern half (Table 2). It is worth noting that regions with deficient and permanent precipitation emerged during the second period (1999–2019) within this region around Lake Urmia in the northwest, as well as at various points in the north and northeast. The lowest variability has also occurred in the water resource region with deficient and permanent precipitation, with a decrease of −0.12%. The region with deficient and concentrate precipitation has extended toward the north, also involving the northern part of Khuzestan Province in the southwest, the center, and the northeastern borders. The only region that has shifted from a region with deficient and concentrate precipitation to one with deficient and permanent precipitation is located on the shores north of the Oman Sea and east of the Strait of Hormuz. This indicates a greater distribution of rainy days per unit of time over the year in the region, which calls for further investigation to address emerging questions. The shift in water resource distribution can be attributed to a decrease in precipitation concentration and an increase in temporal consistency of rainy days along the northern coasts of the Oman Sea. This is due, in turn, to the rising sea temperatures (Khan et al. 2004; Pionkovski & Chiffings 2014; Bahri & Khosravi 2020), increased specific humidity along the southern coasts of Iran in recent years (Dehghani et al. 2018; Darand et al. 2019), consistent with an increase in fall precipitation along the southeastern coasts of the country (Mosaffa et al. 2020), integrated moisture flux convergence from the Oman Sea and Arabian Sea, as well as other relevant trends. The area of abundant and concentrate water resources has also decreased during this second period, mainly in the southern part of the Zagros Mountains in the south of 30°N, and in the highlands of Lalehzar in Kerman Province at 57°E. Despite a decrease of 1.44% in its area, it has expanded toward northern latitudes to cover parts of Iran's western border between 34°N and 35°N.

The analysis of maps displaying the trends in the H-Index and its variability demonstrates that the variability in their values is distributed all over the country unlike what has been observed on the maps for the mean. Thus, the range of the significant negative trend is greater than that of the positive trend based on the H-Index. Moreover, the maximum significant negative trend is observed with a decreasing rate of 0.15 bits per decade at the southeastern corner in the east and north of the Persian Gulf coasts. In contrast, the maximum positive trend is observed with the same intensity to the north of the Oman Sea coasts and along the Alborz Mountains in the north. The trend in the D-Index is exactly inverse to that in the H-Index, indicating an increase in the consistency and reliability of precipitation occurrence for regions with positive trends in the H-Index. Conversely, there is a decrease in temporal distribution and an increase in precipitation concentration for regions with negative trends. Given a significant sudden change in the frequency of rainy days and H-Index values in 1998, we divided the long-term period (1962–2019) into two periods: before and after 1998. We compared the precipitation index and parameter values between these two periods. It was found that after 1998, values of the H-Index, the frequency of rainy days, and mean precipitation have decreased, while the D-Index value has increased. These results are consistent with an incremental trend in severe and pervasive droughts in Iran in recent years (Keshavarz et al. 2012; Hosseini et al. 2021).

In the following step, Iran was divided into four regions based on water resources, taking into account the values of the H-Index and the D-Index as well as annual precipitation. These regions were categorized as follows: abundant and permanent, deficient and permanent, deficient and concentrate, and abundant and concentrate. Comparing and analyzing these water resource regions in terms of the H-Index before and after 1998 revealed significant changes during the second period (1999–2019). The regions with abundant and permanent, deficient and permanent, and abundant and concentrate precipitation became less extensive, while the regions with deficient and concentrate precipitation expanded toward northern latitudes as well as areas in the center, northeast, and southwest. The most significant reduction occurred in the abundant and permanent water resource region, with a decrease of 2.97% in the country's northern half. It is crucial to note that parts of the abundant and permanent region in the northwestern corner, along with other scattered areas in the northern half of the country, shifted to the region with deficient and permanent precipitation. This shift could have negative consequences on the hydrologic cycle and available water resources in those regions. To meet preeminent water needs, careful and early water management strategies must be implemented to reduce water waste and store excess water during the rainy season (Mishra et al. 2009). According to Fathian et al. (2020), there has been a decreasing trend in precipitation and its intensity and also an incremental trend in the frequency of consecutive days without precipitation in recent years over the western, northern, and northwestern parts of Iran. HadiPour et al. (2020) addressed the decreasing trend in precipitation over more than 11% of the north half of the country, as well as a decrease of 14 mm per decade over semi-arid regions in the northwest during the past decade.

Furthermore, in the western part of the Alborz Mountains at 35°N and 50°E, there has been a shift from a region with deficient and permanent precipitation to an abundant and permanent region during the second period. In contrast, regions to the north of the Oman Sea coasts have shifted from an abundant and concentrate region to one with deficient and permanent precipitation. These shifts indicate a decrease in precipitation concentration and an increase in the temporal distribution of rainy days throughout the year. The spatial distribution of the water resource regions identified by the D-Index was the same as that for the H-Index, differing only in the variability in the extension of the areas. Thus, it was only the region with deficient and permanent precipitation that became more extensive during the second period in terms of the precipitation D-Index, while the abundant and concentrate region experienced the highest decrease in extension, with a rate of −3.09%. In conclusion, it can be stated that variability has increased in Iran's water resource regions, particularly in arid and low-precipitation areas, moving toward the northern half and reducing the extension of high-precipitation humid areas. These changes are characterized by an increase in deficient and concentrate regions and a decrease in abundant and permanent precipitation regions. These changes in climatic elements, including temperature, can mainly be attributed to negative human activities and climate change, resulting in significant decreases in water resource conditions and precipitation patterns worldwide (Westra et al. 2013; Grill et al. 2015). Another important consequence of regional warming and Iran's climate change, especially in recent decades, is an upward trend in temporal precipitation concentration and an increase in the frequency of extremely rainy days (Vaghefi et al. 2019; Tegegne et al. 2021).

The current study aimed to identify the spatiotemporal variability in monthly precipitation and specify the water resource regions over Iran by applying the entropy method (H-Index) and its variability (D-Index). To do this, daily precipitation data from 01/01/1962 to 31/12/2019 with a spatial resolution of 0.25° × 0.25° were used. The following conclusions are drawn from this study:

• (1)

  The entropy value (H-Index) is varied over Iran from 1.6 bits in the southern coasts, southwest, and eastern half of the country to 3.4 bits along the Caspian coasts, and the western half along the Zagros Mountains.

• (2)

  The analysis of the spatial correlation demonstrated a direct relationship over Iran between latitude, precipitation, and the frequency of rainy days on one hand, and the H-Index on the other. This relationship was inversely related to longitude.

• (3)

  It was found that after 1998, values of the H-Index, the frequency of rainy days, and mean precipitation have decreased, while the D-Index value has increased.

• (4)

  Coupling of the values of the H-Index and D-Index with annual precipitation enables detection of the potential availability of water resources. Based on these values, Iran was divided into four distinct regions: abundant and permanent, deficient and permanent, deficient and concentrate, and abundant and concentrate.

• (5)

  Comparing the H-Index value before and after 1998 revealed significant changes over water resource regions during the second period (1999–2019). The regions with abundant and permanent, deficient and permanent, and abundant and concentrate precipitation became less extensive, while the regions with deficient and concentrate precipitation expanded toward northern latitudes as well as areas in the center, northeast, and southwest. It is crucial to note that parts of the abundant and permanent region in the northwestern corner, along with other scattered areas in the northern half of the country, shifted to the region with deficient and permanent precipitation.

We extend our sincere gratitude to Professor Seyed Abolfazl Masoodian for providing daily gridded precipitation data from the Asfazari database.

M.D. studied and worked on conceptualization and methodology, wrote the original draft, and reviewed and edited the manuscript. F.P. worked on formal analysis, data collection, conceptualization, and analysis. All authors read and approved the final manuscript.

This work is based upon research funded by the Vice Chancellorship of Research and Technology, University of Kurdistan.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.