In recent decades, human activities such as the excessive production of carbon dioxide gas, deforestation, overexploitation of natural resources, and so on have caused changes in the climate regimes and frequent occurrence of droughts. Thus, the investigation of the trend of changes in drought can be effective in better understanding the drought condition and also more properly managing the adverse effects of drought. Therefore, in this study, the trend of changes in drought was assessed based on the standardized precipitation index (SPI) and the spatially normalized SPI (SN-SPI) in 34 stations over Iran on 1-, 3-, 6-, and 12-month time scales from 1967 to 2019 using the XI correlation technique (XICOR). Then, using the mean residual error (MRE) index and also a comparison of the correlation coefficient (CC) between the SPI and SN-SPI values with a perfect reliable line (line with the equation Y=X- or T-Statistics index), the performances of the SPI and SN-SPI were investigated. The results of the trend assessment indicated that the SPI and SN-SPI had almost the same performance in all chosen time scales (including 1-, 3-, 6-, and 12-month). However, the results of the T- Statistics and MRE revealed that the calculated values of the SN-SPI in more than 80% of the chosen stations (in the selected time scales) were different from the SPI, and in more than 70% of stations, the calculated values of the SN-SPI were less than the SPI. Therefore, it can be said that the SN-SPI has a different performance from the SPI, and under the influence of spatial normalization of the precipitation values in the SN-SPI, the overall level of the calculated SN-SPI values will be decreased.

  • The XICOR as a new method was used to assess the trend of change.

  • The SN-SPI and the SPI were used to estimate drought conditions.

  • In this research, data series of 34 stations with various climate conditions were used.

  • In this research, the performance of the SN-SPI and SPI was compared.

Graphical Abstract

Graphical Abstract
Graphical Abstract

The meteorological drought can occur in any region with any climatic conditions, from hyper-arid (HyA) to hyper-humid (Afshar et al. 2022; Band et al. 2022; Wang et al. 2022). This phenomenon has directly or indirectly adverse effects on various sectors such as food security, socio-economic security, migration rate, unemployment rate, and so on (Shamshirband et al. 2020; Chukwudum & Dioggban 2022; Qin et al. 2022; Shahpari et al. 2022). The negative impacts of drought are more severe in countries with more arid climate conditions, countries with lower access to surface and subsurface water resources, and less developed countries with weaker economic potential (Bahrami et al. 2020; Zarei et al. 2021; Yazdi et al. 2022). In recent decades, affected by various factors, especially improper anthropogenic activities (without attention to the principles of sustainable and adaptable development) such as overproduction of CO2, some problems such as global warming, polar refrigerator melting, and so on have occurred (Rahman et al. 2021; Letcher 2022). This has led to changes in global weather regimes (Espoir et al. 2022; Monerie et al. 2022). So, the temporal and spatial patterns of droughts’ occurrence and severity have also changed (Afshar et al. 2022; Zhang et al. 2022). Therefore, paying attention to the trend of changes in drought can be effective in fully understanding the drought situation and managing its adverse impacts. Many indicators have been introduced for evaluating and monitoring drought situations worldwide. The standardized precipitation index (SPI) is one of the most widely used indices in the world due to its user-friendly structure, low need for climatic variables (rainfall only), and ability to determine the severity of drought at different time scales such as 1-, 3-, 6-, 9-, 12-, and 24- month (Sahana et al. 2021; Khanmohammadi et al. 2022; Noguera et al. 2022; Salvacion 2022).

Abro et al. (2022) evaluated the trend of the SPI in the Qinhuai River Basin using the Mann–Kendall (MK) and Sen's slope (Ss) tests. This research showed that the SPI, in January and September, had significant increasing and decreasing trends, respectively. Moazzam et al. (2022) used the SPI and the MK trend test to assess the spatiotemporal drought in South Korea. According to the results, the drought severity had a decreasing trend in January, March, April, May, June, and August and an increasing trend in September, October, and December. Khanmohammadi et al. (2022) assessed the trend of the changes in the SPI using the MK trend test over Iran from 1960 to 2014 and showed that the SPI had a downward trend in most chosen stations. The downward trend of slope in the SPI in the northwest and west regions of Iran was more severe. Liu et al. (2021) evaluated the spatiotemporal drought based on the SPI using the MK and multivariable linear regression tests in Sichuan, China. Based on the results, the drought intensity had increased in the western regions of the study area. Tuan & Canh (2021) assessed the trend of changes in the SPI using the MK and Ss trend tests in Vietnam based on the data series of 11 stations during 1986–2016. The results indicated that drought has an increasing trend in the study area.

In recent decades, the SPI has been used to assess drought in many studies worldwide (Lottering et al. 2020; Achite et al. 2022; Samantaray et al. 2022). But, at first, the diversity in climatic, topographic, and environmental factors has an influential role in changing the spatially normalized precipitation (SNP) in large basins (Chaolin et al. 2005; Djebou et al. 2014; Zarei & Moghimi 2019; Mokarram et al. 2020) and also the SPI. This issue can lead to the hypothesis that comparing the calculated SPI in different regions with different climatic and topographic conditions without attention to the SNP is correct or not. This hypothesis was first proposed by Koutroulis et al. (2011) about the SPI. They proved that to provide a better possibility to compare the calculated SPI, especially in large basins, attention to SNP is vital and essential. Therefore, Koutroulis et al. (2011) have introduced a modified version of the SPI named the spatially normalized SPI (SN-SPI). In the SN-SPI, the precipitation has been replaced with SNP.

On the other hand, in real-world problems, scientists may be interested in measuring the dependency of two variables. To achieve this goal, there are several parametric and non-parametric techniques. The Pearson, Spearman's ρ, MK, Ss, and Kendall's τ tests are some of the most famous classical measures of statistical association (Zarei et al. 2015; Cao et al. 2022; Foroumandi et al. 2022; Uwimbabazi et al. 2022). These coefficients are very powerful for detecting linear or monotone associations. However, the big problem is that they are not effective for detecting associations that are not monotonic, even in the complete absence of noise. In this research, for the first time, we apply a new coefficient of correlation, defined by Chatterjee (2021) and called XICOR, to measure the dependency of variables.

Finally, according to all of the mentioned issues, the objectives of this research are (a) assessing the condition and the changes in the trend of drought in 34 synoptic stations over Iran during 1967–2019 based on the SPI and SN-SPI (the main advantage of SPI and SN-SPI is that they can only be calculated using rainfall) in 1-, 3-, 6-, and 12-month time scales (to compare the better performance of indices in short- and long-term time scales) using the XICOR technique and (b) the comparison of the performance of the SPI and SN-SPI in different time scales based on the comparison of the correlation coefficient (CC) between the values of the SPI and SN-SPI with a perfect reliable line (based on the T-Statistics index) and the mean residual error (MRE) index at all stations. Some aspects of research innovation include using the SN-SPI for assessing the drought situation in addition to the SPI; using the XICOR for the trend assessment for the first time; and comparing the performance of the SN-SPI and SPI using the T-Statistics technique.

Study area

The study area of this article is Iran country with an area of about 1.648 million km2 and a population of around 85 million. This country is located in the southwest of Asia between latitude 25.05°–39.78 °N and longitude 44.08°–63.30 °E and bounded by Turkey, Iraq, Oman, Persian Gulf, Afghanistan, Pakistan, Turkmenistan, Azerbaijan, Armenia, and the Caspian Sea. The mean altitude of the study area is 2,787.5 m. The mean annual precipitation and potential evapotranspiration parameters are 361.55 and 1,806.41 (mm year−1), respectively. Also, the mean annual temperature is 17.85 °C. Most of Iran has hyper-arid (HyA), arid (Ar), and semi-arid (SeA) climate conditions (Zarei & Masoudi 2019). Petroleum, gas, petrochemicals, coal, metal minerals, and so on are some of the most critical natural resources, and wheat, barley, rice, corn, cotton, and fruit trees are some of the most important agricultural products of Iran. About 10.98% of Iran's area is forest. The main occupation of the Iranian people is agriculture, animal husbandry, and service activities. The spatial position map, land-use map, Isohyetal map, and some meteorological properties of chosen stations in Iran are presented in Table 1 and Figure 1.
Table 1

Some climatic and spatial properties in chosen stations based on climatic data series from 1967 to 2019

StationLatitude (N)Longitude (E)Altitude (m)Mean annual T (°C)Mean annual R (mm)Mean annual PET (mm)Climate conditiona
Ahvaz 31.344 48.744 22.5 25.76 231.39 2,404.34 Ar 
Arak 34.072 49.783 1,702.8 13.99 326.64 1,509.51 SeA 
Babolsar 36.720 52.653 −21.0 17.35 917.05 1,145.01 Hu 
Bandar Abbas 27.214 56.373 9.8 26.98 173.95 2,404.93 Ar 
Bandar Anzali 37.480 49.458 −23.6 16.48 1,766.16 1,161.10 Hu 
Bandar Lenge 26.528 54.828 22.7 26.86 134.13 2,478.94 Ar 
Birjand 32.891 59.283 1,491.0 16.49 160.68 2,087.34 Ar 
Bushehr 28.904 50.821 8.4 25.01 248.00 2,159.76 Ar 
Chabahar 25.281 60.651 8.0 26.33 113.20 2,045.66 Ar 
Esfahan 32.517 51.706 1,550.4 16.58 128.86 1,707.60 Ar 
Fassa 28.899 53.719 1,268.0 19.43 285.55 1,867.72 Ar 
Ghazvin 36.319 50.020 1,279.1 14.07 319.47 1,534.17 SeA 
Gorgan 36.905 54.413 0.0 17.77 565.91 1,270.16 SeA 
Iran Shahr 27.229 60.718 591.1 26.95 109.82 2,365.56 HyA 
Kerman 30.256 56.962 1,754.0 16.02 134.85 2,129.20 Ar 
Khoy 38.558 44.995 1,103.4 12.25 293.04 1,223.03 SeA 
Mashhad 36.236 59.631 999.2 14.80 255.32 1,653.98 Ar 
Oroomieh 37.659 45.055 1,328.0 11.36 330.65 1,361.92 SeA 
Ramsar 36.904 50.683 −20.0 16.29 1,232.50 1,030.10 Hu 
Rasht 37.203 49.645 24.8 16.23 1,313.82 1,090.93 Hu 
Sabzevar 36.207 57.649 962.0 17.91 192.73 2,122.53 Ar 
Sanandaj 35.254 47.015 1,373.4 13.80 440.77 1,006.19 SeA 
Saqez 36.222 46.311 1,522.8 11.17 485.47 1,470.99 SeA 
Semnan 35.588 53.421 1,127.0 18.29 139.86 2,402.67 Ar 
Shahre Kord 32.292 50.839 2,048.9 11.66 325.83 1,463.61 SeA 
Shiraz 29.561 52.603 1,488.0 18.08 319.11 1,935.79 Ar 
Tabass 33.603 56.951 711.0 22.16 82.10 1,884.86 HyA 
Tabriz 38.122 46.242 1,361.0 12.88 274.55 1,719.15 Ar 
Tehran 35.693 51.309 1,191.0 17.79 236.82 1,891.51 Ar 
Torbat Hydarieh 35.332 59.206 1,451.0 14.40 261.22 2,082.52 Ar 
Yazd 31.904 54.289 1,230.2 19.65 56.81 2,135.38 HyA 
Zabol 31.089 61.543 489.2 22.41 54.58 3,383.98 HyA 
Zahedan 29.472 60.900 1,370.0 18.72 78.44 2,307.37 HyA 
Zanjan 36.660 48.522 1,659.4 11.26 303.57 980.73 SeA 
StationLatitude (N)Longitude (E)Altitude (m)Mean annual T (°C)Mean annual R (mm)Mean annual PET (mm)Climate conditiona
Ahvaz 31.344 48.744 22.5 25.76 231.39 2,404.34 Ar 
Arak 34.072 49.783 1,702.8 13.99 326.64 1,509.51 SeA 
Babolsar 36.720 52.653 −21.0 17.35 917.05 1,145.01 Hu 
Bandar Abbas 27.214 56.373 9.8 26.98 173.95 2,404.93 Ar 
Bandar Anzali 37.480 49.458 −23.6 16.48 1,766.16 1,161.10 Hu 
Bandar Lenge 26.528 54.828 22.7 26.86 134.13 2,478.94 Ar 
Birjand 32.891 59.283 1,491.0 16.49 160.68 2,087.34 Ar 
Bushehr 28.904 50.821 8.4 25.01 248.00 2,159.76 Ar 
Chabahar 25.281 60.651 8.0 26.33 113.20 2,045.66 Ar 
Esfahan 32.517 51.706 1,550.4 16.58 128.86 1,707.60 Ar 
Fassa 28.899 53.719 1,268.0 19.43 285.55 1,867.72 Ar 
Ghazvin 36.319 50.020 1,279.1 14.07 319.47 1,534.17 SeA 
Gorgan 36.905 54.413 0.0 17.77 565.91 1,270.16 SeA 
Iran Shahr 27.229 60.718 591.1 26.95 109.82 2,365.56 HyA 
Kerman 30.256 56.962 1,754.0 16.02 134.85 2,129.20 Ar 
Khoy 38.558 44.995 1,103.4 12.25 293.04 1,223.03 SeA 
Mashhad 36.236 59.631 999.2 14.80 255.32 1,653.98 Ar 
Oroomieh 37.659 45.055 1,328.0 11.36 330.65 1,361.92 SeA 
Ramsar 36.904 50.683 −20.0 16.29 1,232.50 1,030.10 Hu 
Rasht 37.203 49.645 24.8 16.23 1,313.82 1,090.93 Hu 
Sabzevar 36.207 57.649 962.0 17.91 192.73 2,122.53 Ar 
Sanandaj 35.254 47.015 1,373.4 13.80 440.77 1,006.19 SeA 
Saqez 36.222 46.311 1,522.8 11.17 485.47 1,470.99 SeA 
Semnan 35.588 53.421 1,127.0 18.29 139.86 2,402.67 Ar 
Shahre Kord 32.292 50.839 2,048.9 11.66 325.83 1,463.61 SeA 
Shiraz 29.561 52.603 1,488.0 18.08 319.11 1,935.79 Ar 
Tabass 33.603 56.951 711.0 22.16 82.10 1,884.86 HyA 
Tabriz 38.122 46.242 1,361.0 12.88 274.55 1,719.15 Ar 
Tehran 35.693 51.309 1,191.0 17.79 236.82 1,891.51 Ar 
Torbat Hydarieh 35.332 59.206 1,451.0 14.40 261.22 2,082.52 Ar 
Yazd 31.904 54.289 1,230.2 19.65 56.81 2,135.38 HyA 
Zabol 31.089 61.543 489.2 22.41 54.58 3,383.98 HyA 
Zahedan 29.472 60.900 1,370.0 18.72 78.44 2,307.37 HyA 
Zanjan 36.660 48.522 1,659.4 11.26 303.57 980.73 SeA 

Note. T, R, and PET are temperature, rainfall, and potential evapotranspiration (based on the FAO Penman–Monteith equation), respectively.

aThe climate conditions were determined using the UNEP aridity index (Ebrahimi-Khusfi et al. 2022), and HyA, Ar, SeA, Me, and Hu are hyper-arid, arid, semi-arid, Mediterranean, and humid climate conditions, respectively.

Figure 1

Study region. Note. (a) Climate conditions and distribution of chosen stations, (b) isohytal map, and (c) land-use map.

Figure 1

Study region. Note. (a) Climate conditions and distribution of chosen stations, (b) isohytal map, and (c) land-use map.

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Data collection and data evaluation

To compute the SPI and SN-SPI, the precipitation data series of 34 stations over Iran from 1967 to 2019 at 1-, 3-, 6-, and 12-month time scales were used (Table 1). The mentioned data were provided by Iran's meteorological organization (www.irimo.ir). In this research, an attempt was made to select and use a sufficient number of stations (34 stations) with adequate statistical time duration (i.e., 53 years) and appropriate spatial distribution (distributed over an area of about 168 million hectares), and high climatic diversity (5 stations with the HyA climate condition, 16 stations with the Ar climate condition, 9 stations with the SeA climate condition, and 4 stations with the humid climate condition). Therefore, before using the data series, at all stations, the rainfall data series were evaluated, and the missing values of the precipitation were estimated using the Fuzzy regression method based on the correlation between adjacent stations with minimum spatial distance and maximum climatic and topographic similarity (Sadatinejad et al. 2011). The adequacy of the time duration of the rainfall data series and their homogeneity were assessed via the Mockus equation and the Run-test method, respectively (Mahdavi 2002). In general, it can be said that the main reasons for choosing Iran as the study area are the large area of Iran, diversity in topographical conditions, diversity in climatic conditions, diversity in altitude, and so on, which are all effective in changes of precipitation in large watersheds. The main reason for choosing the period from 1967 to 2019 is that we tried to select the maximum possible length of the period of time. Naturally, with the increase in the period of time, the results become more accurate and reliable.

The SPI

The SPI is based on the rainfall variable at different time scales such as 1, 3, 6, and 12 months. It was introduced by McKee et al. (1993). Equations (1) and (2) were used to calculate the SPI. The details of calculating the SPI can be referred to Khanmohammadi et al. (2022), and Lotfirad et al. (2022).
(1)
(2)
where are constant coefficients and is the gamma function.

The SN-SPI

The SN-SPI is based on the normalization of the SPI calculated values. To calculate the SN-SPI, at first, the SPI values will be modified according to the relative average rainfall of the study area at chosen time scales based on and coefficients. Then, the SN-SPI will be computed based on the rescaling of the calculated modified SPI values () (to meet the scale of SPI) based on the and coefficients (Koutroulis et al. 2011).
(3)
(4)
(5)
(6)
(7)
(8)
where and are the average rainfall for each station and average rainfall for all stations at the selected time scales, the and are the maximum and minimum values of the calculated SPI in all stations at chosen time scale, respectively. The and are the maximum and minimum values of the calculated in all stations at the selected time scale, respectively.

The classification of drought severity based on the SN-SPI and the SPI is presented in Table 2.

Table 2

Classification of drought severity based on the SN-SPI and SPI (Koutroulis et al. 2011; Azizi & Nejatian 2022)

Drought classesSymbolRange of changes in SN-SPI and SPI
Extremely dry E-D Less than −2 
Severely dry S-D −1.5 to −1.999 
Moderately dry M-D −1 to −1.499 
Normal and non-drought −0.99 to 0.99 
Moderately wet M-W 1–1.499 
Severely wet S-W 1.5–1.999 
Extremely wet E-W More than 2 
Drought classesSymbolRange of changes in SN-SPI and SPI
Extremely dry E-D Less than −2 
Severely dry S-D −1.5 to −1.999 
Moderately dry M-D −1 to −1.499 
Normal and non-drought −0.99 to 0.99 
Moderately wet M-W 1–1.499 
Severely wet S-W 1.5–1.999 
Extremely wet E-W More than 2 

The XI correlation

The XI correlation was defined by Chatterjee (2021) and called XICOR to measure the dependency of variables.

Assume are random samples of a bivariate random vector The XICOR statistic can be computed as follows:

At first, sort the pairs as where Assume . In other words, is equal to the number of j for which The XICOR is defined by
(9)
Chatterjee (2020) proved that if the random variables X and Y are independent and Y is continuous, then the statistical distribution of
(10)
is approximately standard normal. Chatterjee & Holmes (2020) wrote an R package, named XICOR, to compute and P-values for testing independence between variables. The main advantage of the XICOR method is that this method, in addition to being simple and user-friendly, it is applicable in normal and non-normal data series (without attention to their normality).

Comparison of the performance of the SPI and SN-SPI

In this research to compare the performance of the SPI and SN-SPI, in the first step, the similarity of the calculated values of SPI and SN-SPI was compared using the comparison of the CC between the SPI and SN-SPI at different time scales with the perfect reliable line (Y=X) based on the T-Statistics index. If the |T-Statistics| was less than 1.96, the CC between the SPI and SN-SPI values has no difference with the perfect reliable line at the 0.05 significant level (Turco et al. 2017). The advantage of the T-Statistics method is that in this method, in addition to comparing the correlation between the data series, the changes in each data (the observed value of each data with its predicted value) are also examined and compared separately. In addition, in this method, the significance level of data similarity can also be calculated. In the next step, the MRE index was used to compare the results of the SPI and SN-SPI to determine the overestimation or underestimation of one index compared to another (especially in cases where the calculated absolute values of the T-Statistics were more than 1.96). The positive values of MRE showed that the calculated drought values based on the SN-SPI are more than the computed drought values based on the SPI and conversely (Zarei & Mahmoudi 2020). The schematic flowchart of all research steps is presented in Figure 2.
Figure 2

A schematic flowchart of all research steps.

Figure 2

A schematic flowchart of all research steps.

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Calculating the SPI and SN-SPI

The results of the calculated values of the SPI and SN-SPI indicated that based on both of these, the normal (N) class of drought severity has the most occurrence frequency at all selected stations and all under-evaluation time scales. Based on the results, the occurrence frequency of the N class of drought based on the SN-SPI was more than the SPI at all stations and all time scales, whereas the occurrence frequencies of extremely dry (E-D), severely dry (S-D), extremely wet (E-W), and severely wet (S-W) classes based on the SN-SPI were less than the SPI at all stations and all time scales. It seems that the leading cause of this issue is the normalization of the SPI to calculate the SN-SPI (Figures 3 and 4). Koutroulis et al. (2011) showed that the occurrence frequencies of the E-D, S-D, E-W, and S-W classes of drought based on the SN-SPI were less than those on the SPI (similar to our study results). Based on the results, it seems that with the spatial normalization of the amount of precipitation, the impact of rare rainfall values (very low and very high amounts of rainfall) on drought indices has been reduced, and the comparison of drought intensities between the investigated stations (in 100% of the chosen stations) becomes more accurate. Surveys showed that, based on both indices, the years 2008 and 2010 were the driest years from 1967 to 2019. In those years, almost all stations suffered from drought, and in many of them, the drought that occurred was the most severe drought from 1967 to 2019 (Figure 5 and Tables S1 and S2). According to the results, during 1967–2019, drought occurred in all stations, but in recent years (around after 2000), the occurrence frequency of droughts increased in almost all stations. The main reason for this issue could be the decrease in rainfall caused by the downward trend (drying trend) in Iran's climate conditions in the long term (Masoudi & Elhaeesahar 2016; Zarei & Masoudi 2019).
Figure 3

The calculated SN-SPI in some of the chosen stations and some of the selected time scales.

Figure 3

The calculated SN-SPI in some of the chosen stations and some of the selected time scales.

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Figure 4

The calculated SPI in some of the chosen stations and some of the selected time scales.

Figure 4

The calculated SPI in some of the chosen stations and some of the selected time scales.

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Figure 5

Occurrence frequency of SPI and SN-SPI classes in the selected stations from 1967 to 2019 in the 12-month time scale.

Figure 5

Occurrence frequency of SPI and SN-SPI classes in the selected stations from 1967 to 2019 in the 12-month time scale.

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The trend of the SN-SPI changes

The results of the trend of the SN-SPI changes from 1967 to 2019, using the XICOR, on the 1-month time scale showed that in different monthly time periods, the trend of changes in the calculated SN-SPI in 41.18–79.41% of the chosen stations is decreasing (Table S3). Based on the results, on the monthly time scale, the trend of changes in the SN-SPI was significant at the 5% level at 5.88– 26.47% of the chosen stations on the various monthly periods. It seems that the occurrence frequency of drought in warmer months such as August and September is higher than that in other months. The main reason for this could be more rainfall fluctuations in these months (Table S3).

According to the results, at the 3-month time scale, the calculated SN-SPI had a downward trend at 23.53, 58.82, 73.53, and 58.82% of the selected stations in the winter, spring, summer, and autumn periods, respectively. On the other hand, the trend of changes in the SN-SPI was significant at the 5% level at 11.76, 8.82, 8.82, and 8.82% of the chosen stations in the winter, spring, summer, and autumn periods, respectively. Appearing on a seasonal time scale compared to monthly, the number of stations with a decreasing trend in the SN-SPI has reduced. This indicates the non-uniform distribution of the rainfall in the months of each season (Figure 6 and Table S4).
Figure 6

The trend of changes in the SN-SPI and SPI at chosen stations in the 3-, 6-, and 12-month time scales based on the XICOR. Note. In all stations, the XICOR absolute value equal to or more than 0.144 shows a significant trend at the 5% significant level.

Figure 6

The trend of changes in the SN-SPI and SPI at chosen stations in the 3-, 6-, and 12-month time scales based on the XICOR. Note. In all stations, the XICOR absolute value equal to or more than 0.144 shows a significant trend at the 5% significant level.

Close modal

The results of the trend of the SN-SPI changes on the 6- and 12-month time scales revealed that the calculated SN-SPI had an increasing trend in the least 60% of the selected stations, and also, the trend of changes in the 6- and 12-month SN-SPI was significant at the 5% level at the 23.53.76, 8.82, and 8.82% of the chosen stations first 6-month, second 6-month, and annual periods, respectively (Figure 6 and Table S4).

The trend of the SPI changes

The calculated XICOR for the trend of SPI changes from 1967 to 2019 on the 1-, 3-, 6-, and 12-month time scales indicated that the SPI had a decreasing trend at 26.47–85.29% of the chosen stations on the various time periods. The results revealed that, based on the SPI, the number of stations with significant trends in all time scales is almost similar to the SN-SPI. According to the results, the calculated trend of changes based on the SPI and SN-SPI has no significant difference. It showed that spatial normalization of the rainfall values had a uniform effect on the rainfall values and computed the drought index (SN-SPI). Indeed, the closeness of the calculated XICOR values based on the SPI and SN-SPI from 1967 to 2019 is not the reason for the similarity of the calculated SPI and SN-SPI values (Figure 6 and Tables S5 and S6). Bari Abarghouei et al. (2011) assessed the trend of changes in the SPI based on the climatic data series of 42 stations over Iran during 1975–2005 using the MK test. This research indicated a negative trend of SPI in many stations in Iran. It seems that the findings of this study are different from the results of our research. The reasons for these are (a) the difference in the chosen periods (we examined 53 years), (b) the difference in the used trend test, and (c) the sensitivity of the MK method to the normality of the data series (the XICOR method is not sensitive to the normality of the data series). Due to the existence of the return period in climatic phenomena, in climatic research, with an increase in the selected period, the results will be more accurate.

Comparison of the SPI and SN-SPI using the T-Statistics

Even in the percentage of the stations with a decreasing trend in the drought severity and also the percentage of the stations with a significant decreasing trend, there is not much difference between the SPI and SN-SPI on the different time scales. But the overall level of the calculated values by the SPI and SN-SPI was different. Although this difference may not affect the trend of drought changes (based on both indices), it certainly affects the placement of various regions in different drought classes in different years and on different time scales. The results of comparing the CC between the SPI and SN-SPI with the perfect reliable line (Y=X) based on the T-Statistics index showed that at least 79.4% of the chosen stations (on a 12-month time scale) and at most 100% of the selected stations (in the August time scale), the absolute values of the T-Statistics were more than 1.96 (Figure 7 and Tables S7 and S8). In other words, the CC between the calculated values of the SPI and SN-SPI was different with the perfect reliable line (Figure 8). Considering that the T-Statistics index, in addition to examining the significance of the correlation between two data series, also examines the changes of the observed arrays compared to its predicted value; therefore, if the absolute value of the T-Statistics index was more than 1.96, then it is indicated that the data series of the two investigated variables are not similar at the 5% significant level. Therefore, it can be concluded that at most stations (at 79.4–100% of the chosen stations in different time scales), the computed values of the SPI were different from the SN-SPI. Indeed, the main reason for this difference is the spatial normalization of used rainfall data in the SN-SPI. With the spatial normalization of the amount of rainfall, the influence level of the very large and very small amounts of precipitation in the drought index will be reduced. As a result, the overall level of the calculated SN-SPI will be decreased (Koutroulis et al. 2011).
Figure 7

The calculated T-Statistics indicator at chosen stations in the 3-, 6-, and 12-month time scales. Note. If the T-Statistics was less than 1.96, the correlation of SPI and SN-SPI has no difference with the perfect reliable line at the 0.05 significance level.

Figure 7

The calculated T-Statistics indicator at chosen stations in the 3-, 6-, and 12-month time scales. Note. If the T-Statistics was less than 1.96, the correlation of SPI and SN-SPI has no difference with the perfect reliable line at the 0.05 significance level.

Close modal
Figure 8

Comparison of the correlation between the SPI and SN-SPI with the perfect reliable line in some of the chosen stations at the 12-month time scale.

Figure 8

Comparison of the correlation between the SPI and SN-SPI with the perfect reliable line in some of the chosen stations at the 12-month time scale.

Close modal

The results of the MRE indicator

The results of the T-Statistics revealed that at most stations, the calculated values of the SPI were different from the SN-SPI; therefore, to determine the overestimation or underestimation of the calculated values based on the SN-SPI compared to the SPI, the MRE index was used. The results of the MRE index indicated that in at least 53% of the chosen stations (in the March time scale) and at most 85.3% of the selected stations (in the second 6- month time scale), the calculated drought values based on the SN-SPI are less than the computed drought values based on the SPI (Tables 3 and 4). Therefore, it can be argued that under the influence of the spatial normalization of the used climatic data in the SN-SPI, the overall levels of the computed values of drought severity based on the SN-SPI are less than the SPI. The results of research by Koutroulis et al. (2011) also indicated that in all time scales (1-, 3-, 6-, 12-, 24-, and 48-month time scales), the calculated values of drought severity using the SN-SPI are lower than the computed values of drought severity using the SPI (similar to the results of our research).

Table 3

The results of the MRE index between calculated values of the SPI and SN-SPI at chosen stations in the 1-month time scale

StationMRE index
JanFebMarAprMayJunJulAugSepOctNovDec
Ahvaz − − − − − − − − − 
Arak − − − − − − − 
Babolsar − 
Bandar Abbas − − − − − − − − − − − − 
Bandar Anzali − − 
Bandar Lenge − − − − − − − − − − − − 
Birjand − − − − − − − − − − − − 
Bushehr − − − − − − − − − 
Chabahar − − − − − − − − − − − 
Esfahan − − − − − − − − − − − − 
Fassa − − − − − − − − 
Ghazvin − − − − − − − − 
Gorgan − − 
Iran Shahr − − − − − − − − − − − − 
Kerman − − − − − − − − − − − − 
Khoy − − − − − − − − 
Mashhad − − − − − − − − 
Oroomieh − − − − − − − 
Ramsar − − − − 
Rasht − 
Sabzevar − − − − − − − − − − − 
Sanandaj − − − − − − 
Saqez − − − − − − − − − 
Semnan − − − − − − − − − − − − 
Shahre Kord − − − − − − − 
Shiraz − − − − − − − − − 
Tabass − − − − − − − − − 
Tabriz − − − − − − − 
Tehran − − − − − − − − − − − − 
Torbat Hydarieh − − − − − − − − − 
Yazd − − − − − − − − − − 
Zabol − − − − − − − − − 
Zahedan − − − − − − − − − − − − 
Zanjan − − − − − − − − − 
StationMRE index
JanFebMarAprMayJunJulAugSepOctNovDec
Ahvaz − − − − − − − − − 
Arak − − − − − − − 
Babolsar − 
Bandar Abbas − − − − − − − − − − − − 
Bandar Anzali − − 
Bandar Lenge − − − − − − − − − − − − 
Birjand − − − − − − − − − − − − 
Bushehr − − − − − − − − − 
Chabahar − − − − − − − − − − − 
Esfahan − − − − − − − − − − − − 
Fassa − − − − − − − − 
Ghazvin − − − − − − − − 
Gorgan − − 
Iran Shahr − − − − − − − − − − − − 
Kerman − − − − − − − − − − − − 
Khoy − − − − − − − − 
Mashhad − − − − − − − − 
Oroomieh − − − − − − − 
Ramsar − − − − 
Rasht − 
Sabzevar − − − − − − − − − − − 
Sanandaj − − − − − − 
Saqez − − − − − − − − − 
Semnan − − − − − − − − − − − − 
Shahre Kord − − − − − − − 
Shiraz − − − − − − − − − 
Tabass − − − − − − − − − 
Tabriz − − − − − − − 
Tehran − − − − − − − − − − − − 
Torbat Hydarieh − − − − − − − − − 
Yazd − − − − − − − − − − 
Zabol − − − − − − − − − 
Zahedan − − − − − − − − − − − − 
Zanjan − − − − − − − − − 

Note.+ denotes that the calculated drought values based on the SN-SPI are more than the calculated drought values based on the SPI, and−denotes that the calculated drought values based on the SN-SPI are less than the calculated drought values based on the SPI.

Table 4

The results of the MRE index between calculated values of the SPI and SN-SPI at chosen stations in the 3-, 6-, and 12-month time scales

StationMRE index
WinterSpringSummerAutumn6 months (Jan–Jun)6 months (July–Dec)12 months
Ahvaz − − − − − − − 
Arak − − − − − − 
Babolsar − − − 
Bandar Abbas − − − − − − 
Bandar Anzali − − − − − 
Bandar Lenge − − − − − − 
Birjand − − − − − − − 
Bushehr − − − − − − 
Chabahar − − − − − − − 
Esfahan − − − − − − − 
Fassa − − − − − − 
Ghazvin − − − − − 
Gorgan − 
Iran Shahr − − − − − − − 
Kerman − − − − − − − 
Khoy − − − 
Mashhad − − − − 
Oroomieh − − − − − 
Ramsar − − 
Rasht − − 
Sabzevar − − − − − − − 
Sanandaj − − − 
Saqez − − − − − 
Semnan − − − − − − 
Shahre Kord − − − − − 
Shiraz − − − − − 
Tabass − − − − − − 
Tabriz − − − − − 
Tehran − − − − 
Torbat Hydarieh − − − − 
Yazd − − − − − 
Zabol − − − − − − 
Zahedan − − − − − 
Zanjan − − − − − 
StationMRE index
WinterSpringSummerAutumn6 months (Jan–Jun)6 months (July–Dec)12 months
Ahvaz − − − − − − − 
Arak − − − − − − 
Babolsar − − − 
Bandar Abbas − − − − − − 
Bandar Anzali − − − − − 
Bandar Lenge − − − − − − 
Birjand − − − − − − − 
Bushehr − − − − − − 
Chabahar − − − − − − − 
Esfahan − − − − − − − 
Fassa − − − − − − 
Ghazvin − − − − − 
Gorgan − 
Iran Shahr − − − − − − − 
Kerman − − − − − − − 
Khoy − − − 
Mashhad − − − − 
Oroomieh − − − − − 
Ramsar − − 
Rasht − − 
Sabzevar − − − − − − − 
Sanandaj − − − 
Saqez − − − − − 
Semnan − − − − − − 
Shahre Kord − − − − − 
Shiraz − − − − − 
Tabass − − − − − − 
Tabriz − − − − − 
Tehran − − − − 
Torbat Hydarieh − − − − 
Yazd − − − − − 
Zabol − − − − − − 
Zahedan − − − − − 
Zanjan − − − − − 

Note.+ denotes that the calculated drought values based on the SN-SPI are more than the calculated drought values based on the SPI, and – denotes that the calculated drought values based on the SN-SPI are less than the calculated drought values based on the SPI.

Due to the adverse effects of drought on various sectors, and also, changes in the climate regimes around the world (mainly affected by human activities), changes in the occurrence frequency of droughts, and the severity of droughts in different parts of the world, in this research, the changes trend of drought based on the SPI and SN-SPI in 1-, 3-, 6-, and 12-month time scales during 1967–2019 using the XICOR was evaluated over Iran. Then, based on the T-Statistics and MRE indicators, the performance of the SPI and SN-SPI was compared. According to the results in 1-month (average of chosen monthly periods), 3-month (mean of the selected seasons), 6-month (average of chosen 6-month periods), and 12-month time scales, the changes trend of the SN-SPI in 58.58, 53.68, 34.27, and 26.47% and the changes trend of the SPI in 58.58, 53.68, 34.85, and 29.41% of the selected stations were decreasing, respectively. The results of the T-Statistics revealed that at different time scales, the calculated values of SN-SPI and SPI are different at 80–100% of the selected stations. On the other hand, based on the results of the MRE index, at the different time scales, at about 53–85% of chosen stations, the calculated values of SN-SPI were less than the SPI. Finally, it is suggested that for a more precise assessment of the SN-SPI capability, this index could be compared with the SPI in different situations, for example, based on the replacement of the spatially normalized precipitation with effective spatially normalized precipitation.

The authors would like to thank all sections of the national meteorological organization of Iran for their kind help to provide necessary meteorological data.

The participation of M.M.G. and A.R.Z. includes the data collection, analyzing the results, and writing the article, and the participation of M.M. includes helping to analyze the results.

The author confirms that this article is based on original research and has not been published or presented previously in any journal or conference in any language (in whole or in part).

No funds, grants, or other support were received.

The codes used in this research (using the R 3.6.3 software) are available with the corresponding author and can be shared upon reasonable request.

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

The authors declare there is no conflict.

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