Introduction

Assessing and studying drought globally or in specific areas recently due to global warming, change in rainfall, and their impact on social welfare have become very important) Vlăduţ and Licurici 2020). Food and water resources are highly dependent on the climate (Allen et al. 2019). Water shortage due to the increased environmental risks caused along with the climate changes is the most crucial factor of limiting the development in many areas. Therefore, it is necessary to assess the shortage of water and water resources to predict the appropriate strategies to control the drought in vulnerable areas (Moral et al. 2016). In most countries, global warming has led to severe changes in climatic phenomena such as changes in the type and amount of precipitation, increase destructive floods frequency, and changes in droughts frequency and severity. Therefore, analyzing the amounts of humidity from the climatic indicators as an indicator for the water shortage can be helpful (Sivakumar et al. 2005). In the last century, weather and climate changes have been the subject of many scientific studies. The global weather changes due to natural processes and human factors are critical environmental issues that may cause climate changes in the world (Baltas and Mimikou 2005). Therefore, climatic indicators are a reliable tool for weather identification and classification. Climatologists have proposed various indicators to classify the weather and study the humidity in an area that is usually calculated by precipitation, evapotranspiration (ET), and temperature (Tabari and Aghajanloo 2013). Also, the study of the changes in the climate indicators can be a good starting point for the decision-makers using the integrated management of water resources in the area for future periods (Gebremedhin et al. 2018). In this regard, different scientists have done a wide variety of studies, and the results of most of these studies show that different parts of the world are getting warmer and drier (Derdous et al. 2020; Zarei and Masoudi 2019; Paniagua et al. 2019). Vlăduţ and Licurici (2020) assessed drought in a region located in Oltenia (Romania) with 15 stations from 1961 to 2015 using the De Martonne drought index (IDM) at the annual, seasonal, and monthly levels, the combined index of Pinna (IP), and hydrothermal coefficient of Selyaninov. The results obtained by the index of IP showed a humid climate for the whole region. The annual IDM reports semi-humid, humid, and very humid conditions in the plains, east of the region, and the mountainous areas, respectively. IDM results on a monthly scale also showed a maximum of 5 months with semi-arid conditions, which are generally in the summer, September, and October. The same monthly pattern is highlighted by Selyaninov, especially in the mild or slightly dry months of summer and mainly in the plains. Derdous et al. (2020) classified the climate in northern Algeria into 37 meteorological stations using IDM, Amberge, and United Nations Environment Program indices. All three indicators show semi-arid conditions in the region, while the Amberge index had detected more drought. Tabari et al. (2014) studied the spatial and temporal changes of the IDM drought index in Iran (using temperature and precipitation data) in 41 stations for the 40-year period. The results showed that 88% of Iran has arid and semi-arid climates. The trend of IDM was decreasing in 63% of stations. A significant decrease in the trend of the IDM was observed mainly in the western and northwestern regions of the country. The relative change in the drought index of those stations that had a significant decreasing trend was reported to be about 18–54%. Bačević et al. (2017) analyzed drought by using IDM and IP indices in Serbia. The results of their study showed that no change was observed in the drought for 35 years.

Thornthwaite (1948) defines humidity and drought indicators based on the excess water, water shortage, and water requirements of the region. In Serbia, the analysis of IDM and IP drought indices was studied by Radaković et al. (2018) to analyze the drought index. They used average air temperature and rainfall data of 26 meteorological stations for monthly, seasonal, and annual time scales from 1949 to 2015. The results showed that during the studied period, the area has a very humid climate in winter, humid in spring and autumn, and semi-humid in summer. They also concluded that there had been no change in the trend of the drought in central Serbia. In another study, the trend of changes in the drought indices in Iraq was studied for 28 stations using temperature and precipitation data. The results showed that 97% of Iraq has an arid and semi-arid climate. Also, the trend of changes in the IDM in Iraq has been declining. In 1997, many stations had a downward trend in the value of the IDM. Their results also showed that the climate of Iraq has moved toward the drought state year to year (Şarlak and Agha 2018).

Çiçek and Duman (2015) studied the trend of precipitation on the annual and monthly scales in Turkey during 1975–2008 for 83 meteorological stations. They used the Mann–Kendall (MK) test to detect the trend and Sen’s slope estimator to estimate the slope of trend lines. The results showed that the trend of the seasonal and annual precipitation (except autumn) is declining throughout the country. Caloiero et al. (2016), in another study, using precipitation and temperature data, IDM, and nonparametric MK test on a monthly and seasonal scale in the studied period of 1916–2010 in southern Italy (Calabria), studied the effects of climate change on plants. The results showed that changes in the forest are due to climate change. Tsiros et al. (2020) examined the temporal variability of the drought index in Greece during 1900–1997 for several meteorological stations. The analysis was performed for three distinct climatic periods. The results showed that in most areas, the dry conditions were slow but steady. Also, in some areas, the AI values approached the value of the change threshold from the “semi-arid” class to the “dry” class. While for several areas on the west coast, the AI class remained wet and unchanged in all three periods. Tahroudi et al. (2019) studied the long-term analysis of temperature and precipitation at 34 synoptic stations in Iran for 50 years. The result showed that temperature concentration index (TCI) values showed a uniform temperature pattern on the borders of the Persian Gulf, the Gulf of Oman, and the shores of the Caspian Sea. Also, a comparison between precipitation concentration index PCI and TCI indices showed that these two indices were inversely related and the PCI showed a uniform distribution of rainfall in selected stations in Iran. Khalili et al. (2016) studied the PCI index using annual rainfall data of 34 synoptic stations in Iran for 50 years (1991–2010). They analyzed the precipitation trend and PCI index using the MK test after removing the effect of correlation coefficients on annual and seasonal time scales. The result of the PCI index on an annual time scale showed that 50% of stations experienced an upward trend. Also, in winter, which is the rainiest season in Iran, about 64% of stations experienced a downward trend in precipitation, which increased the PCI index.

Drought is one of the hazardous environmental phenomena whose characteristics such as intensity, duration, and spatial expansion are different in various environments; the greater the severity and spatial extent of this climatic hazard, the more severe the effects in different parts. Among natural disasters that have affected human populations, the prevalence of drought in recent decades has been more than other disasters, and that is due to the dry and desert climate in Iran. The inherent shortage of water resources in the country, the occurrence of consecutive droughts in recent years, and the significant increase in the consumption of groundwater resources make it highly necessary to pay more attention to the manner and extent of the effects of droughts in the region. Because different variables are directly or indirectly involved in the occurrence of drought and compared to other natural disasters, it is difficult to determine the exact time this phenomenon begins or ends; therefore, for spatial analysis of droughts, it is very important to provide an indicator that can analyze the drought on a regular scale at the exact time and place. Sirvan river is a vital strategic location. So far, few studies have been conducted using comprehensive and up-to-date data to investigate the changes in drought indices. The aim of this study is the spatial and temporal analysis of IDM, IP, and UNEP drought indices (AI) using nonparametric MK methods and age gradient in the Sirvan river basin. For understanding drought analysis, which is one of the major problems today, such an approach is important. This approach can also have a significant impact on reducing water consumption in the area under investigation.

Study area

The area under investigation includes the Sirvan river basin, which is in the west and south of Kurdistan province, in terms of political divisions, and a small part of it is located in the north of Kermanshah province in Iran (Fig. 1). Sirvan river basin is located in the central part between the geographical coordinates 45°53′ to 48°00′ east longitude and 34°15′ to 35°47′ north latitude. This basin with an area of 8456 km2 is one of the sub-basins of the Persian Gulf, which in terms of geomorphology, mainly includes mountainous units. Climatically, the region generally has a cold-to-Mediterranean mountain climate. The average rainfall, temperature, and evaporation in the intended area are 530.12 mm, 13.73°C, and 150.15 mm, respectively.

Fig. 1
figure 1

Geographic location of evaporation stations in the study area

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Data and methods

In this study, using precipitation and temperature data in the studied period (2002–2018), first, the values of IDM, IP, and AI indices in each station were calculated for each year of the studied period and then examined the trend of changes in these indices by using the MK method during the studied period for each station. Also, the slope of trend lines of each station, for all three indexes, was obtained by nonparametric Sen’s method. After that, the average of the indices during the studied period was plotted on the Sirvan river basin with ArcGis software. Then, the area of different parts of the basin with different climates was obtained.

The amount of drought in an area is calculated based on the proposal of De Martonne (1926). The annual, seasonal, and monthly values of the IDM are obtained from the following equations (De Martonne 1926):

$$ {\mathrm{I}}_{\mathrm{DM}}=\frac{\mathrm{P}}{\mathrm{T}+10},\mathrm{I}{\mathrm{s}}_{\mathrm{DM}}=\frac{4\mathrm{Ps}}{\mathrm{T}\mathrm{s}+10},\mathrm{I}{\mathrm{m}}_{\mathrm{DM}}=\frac{12\mathrm{Pm}}{\mathrm{T}\mathrm{m}+10} $$
(1)

where P, Ps, and Pm are the annual, seasonal, and monthly precipitation (mm), and T, Ts, and Tm are the mean annual, seasonal, and monthly surface air temperatures (°C), respectively. The humidity increases with increasing the values of IDM, IsDM, ImDM, and vice versa. The classification of the IDM is shown in Table 1, with a total of seven types of climate.

Table 1 De Martonne index (IDM) classification (Radaković et al. 2018)
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Pinna combinative index

IP has been presented as a combinative index by Radaković et al. (2018):

$$ {I}_p\kern0.5em =\frac{1}{2}\ \left(\frac{Pma}{Tma+10}+\frac{12\ {P}^{\prime }d}{T{}{}^{^{\prime }}d+10}\right) $$
(2)

where Pma is the annual precipitation (mm), Tma is the mean annual surface temperature (°C), as well as the P′d precipitation (mm), and T′d temperature (°C) of the driest month of the year. This index better describes the areas and seasons that require irrigation according to the rainfall and the temperature of the driest month. Table 2 shows the climatic classification based on the IP.

Table 2 Pinna combinative index (Ip) classification (Radaković et al. 2018)
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UNEP aridity index

The UNEP aridity index (AI) was calculated following the Thornthwaite (1948) approach. Thornthwaite drought index classification is based on two factors: (a) supply of water by precipitation and (b) demand of water for evapotranspiration. Precipitation and evapotranspiration are caused by meteorological phenomena and may be different in terms of quantity and seasonal distribution. In this research, a more simplified equation was used for the calculation of potential evapotranspiration developed by Thornthwaite (1948) as follows:

$$ AI=\frac{P}{PET} $$
(3)

where P is the mean annual precipitation (mm) and PET is the mean average evapotranspiration, which is calculated as follows (Nyamtseren et al. 2018):

$$ PET=1.6\ast {\left(\frac{10{T}_i}{J}\right)}^c $$
(4)

where Ti is the monthly mean temperature (°C); J is the heat index which is constant for a given location and is the sum of 12 monthly index values i, where i = \( {\left(\frac{T_i}{5}\right)}^{1.514} \) (°C); c is an empirically determined exponent which is a function of J, c = 6.75 × 10−7J3 − 7.71 × 10−5J2 + 1.79 × 10−2J + 0.49, °C (Nyamtseren et al. 2018). The climate classification is done using the UNEP (1992). Table 3 shows the climatic classification based on the AI values (Nyamtseren et al. 2018).

Table 3 Classification of climatic regions based on UNEP aridity index (UNEP, 1992)
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Conventional Mann–Kendall test

MK test is a statistical test widely used for the analysis of trends for climatic data (Zhang et al. 2009). The statistic value of S, which shows the sum of all counts, is obtained as follows (Nyamtseren et al. 2018):

$$ S={\sum}_{\mathrm{i}=1}^{n-1}{\sum}_{j=i+1}^n\operatorname{sgn}\left({x}_j-{x}_i\right) $$
(5)

where S is the statistic value for the MK test, xi and xj are the observational values for i and j data, n is the number of data, and sgn(xj−xi) is the function of the sign that is defined as follows:

$$ \operatorname{sgn}\left({x}_j-{x}_i\right)=\left\{\begin{array}{c}1\kern1.25em \left({x}_j-{x}_i\right)>0\\ {}0\kern1.25em \left({x}_j-{x}_i\right)=0\\ {}-1\kern0.75em \left({x}_j-{x}_i\right)<0\end{array}\right. $$
(6)

When n≥8, the statistic value of S is distributed almost normally that the mean is zero, and its standard deviation is defined as follows:

$$ V(S)=\frac{n\ \left(n-1\right)\left(2n+5\right)-{\sum}_{i=1}^n{t}_i\ \left({t}_i-1\right)\left(2{t}_i+5\right)}{18} $$
(7)

where S is the statistic value of MK calculated from Eq. 5, according to values of data. V(S) is the variance of the statistic value of S, and the index i represents the category number i, which has similar data in chronological order. ti is the number of similar values for ith observation, and n is the number of data. The standardized Z statistic test is calculated as follows:

$$ Z=\left\{\begin{array}{c}\ \frac{s-1}{\sqrt{v(s)}}\kern2.5em s>0\kern2.25em \\ {}\kern0.75em 0\kern3.5em s=0\kern2em \\ {}\kern1.25em \frac{s+1}{\sqrt{v(s)}}\kern2.25em s<0\kern3em \end{array}\right. $$
(8)

The standardized MK statistic test of Z follows the standard normal distribution with zero mean and unit variance. The null hypothesis is accepted, provided that the absolute value of calculated Z is less than the standard normal value of Z at the significant statistical α level. In this study, significant statistical levels of 1%, 5%, and 10% were considered. Similarly, if the calculated amount of Z is more than the threshold amount of 1.645, the data trend is assumed to be significant at the 10% level. Otherwise, it is assumed as statistically insignificant. Also, if the calculated amount of Z is more than the amount of 1.96 and 2.33, the data trend is assumed to be significant at 5% and 1% levels, respectively. Otherwise, the null hypothesis that there is a trend in the data is rejected at the desired significance level.

Mann–Kendall test with removing the full effect of significant autocorrelation coefficients

The modified MK test was presented by Hamed and Rao (1998). The effect of all significant autocorrelation coefficients is removed from the time series in this test. First, the autocorrelation coefficient of the orders of k or rk (k from 1 to 1/4 of the number of data) was calculated, and its significance was tested at the level of 10%. If none of the mentioned coefficients is significant, the trend is tested by the conventional method, but on the contrary, if one or more autocorrelation coefficients are significant, their effect is removed from the time series. Details of this method can be found in Kumar et al. (2009).

Estimation of the slope of trend lines by using Sen’s method

Sen’s method is a proper nonparametric method for estimating the slope of trend lines. The value of the slope of trend lines is estimated by using the following equation:

$$ \beta =\mathrm{median}\kern0.5em \frac{\left({x}_j-{x}_i\right)}{j-\mathrm{i}}\kern2.25em \forall i>j $$
(9)

where xi and xj are the values of the data at the times of j and (j > l), respectively. Median (u) means the median of the values of u. If the number of u is even, the median of the data is the arithmetic mean of two values in the middle of the data series related to u in ascending or descending order, and if the number of u is odd, the median of the data is the value in the middle of the data in ascending or descending order. In this method, it is assumed that the data trend is linear, and the unit of trend line slope is equal to the unit of the studied variable unit per year (Theil 1950; Sen 1968).

Calculation of percentage changes in the index

The percentage change can be calculated as follows:

$$ \mathrm{tv}\%=\frac{n\ast \upbeta}{\overline{I}}\ast 100 $$
(10)

where tv% is the total percentage changes of the trend line during the studied period, n is the number of the statistical years used in a given station, β is the slope of the trend line of the index changes in the same station, and \( \overline{I} \) is the average of the station’s index during its statistical years.

Geographical information system (GIS) was used for zoning the region in terms of the average annual rainfall and the average drought indices in this study. Ordinary kriging was used for this purpose because this method provides better results than the other geostatistical methods (Radaković et al. 2018).

Results and discussion

The mean annual temperature (MAT) and the mean annual precipitation (MAP) of the Sirvan river basin for the period 2002–2018 are shown in Fig. 2. Evaporation stations located in the west part of the Sirvan river basin have the greatest amount of precipitation. High precipitation is also seen in the northwest. MAP for the Sirvan river basin has a value of 530.12. The highest precipitation is measured at Zarivar lake station, at the west, reaching 715–811 mm; then, Sarcheshmeh, Ghaleh ji, Janevareh, Palangan, and Negal stations have relatively high precipitation in the range of 415–715 mm. The lowest values of precipitation (336–415 mm) were measured in Hosseinabad and Sarabqamish stations in the east of the Sirvan river basin. MAT for the period of 16 years in the Sirvan river basin is equal to 13.73°C. Stations at higher altitudes have lower MAT. Palangan station has the highest temperature (16.6–17.9°C), and Zarivar lake, Kalji, Pirkhezran, Sarcheshmeh, and Janevareh stations have the lowest temperature (11.8–14.02°C). Table 4 shows the MK statistic values of Z, the slope of trend lines, and the percentage change of IDM, IP, and AI indices in the selected stations of the Sirvan river basin. The results show that in the IDM method, from 10 studied stations, eight stations have negative Z statistic value; among stations with a negative Z statistic value, variations trend for one station (Janevareh) is significant at the level of 10%; in IP method, from 10 studied stations, five stations have a negative Z statistic. Among the stations with a negative Z statistic, the variations trend for one station (Janevareh) is significant at the level of 10%. Also, in the AI method, from 10 studied stations, nine stations have a negative Z statistic value; among the stations with a negative Z statistic value, variations trend for one station (Janevareh) was significant at the level of 10%.

Fig 2
figure 2

Spatial distribution of mean annual precipitation (MAP) and mean annual temperature (MAT) in Sirvan river basin

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Table 4 Mann–Kendall statistic values of Z, the slope of trend lines, and the percentage change of De Martonne, Pinna, and UNEP indices in the selected stations of the Sirvan river basin
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Figure 3 shows the boxplot diagram for the slope of trend lines of various indices changes in the Sirvan river basin stations. As can be seen from the figure, the middle of the slope of trend lines for IDM, IP, and AI indicators are negative and have values of −0.165, −0.09, and −0.006, respectively. This reveals that according to the value of the indicators, a period of decline has occurred during the course of time in which the study was carried out. The top line of the rectangles is almost zero, which shows that except for 25% of the stations have a positive slope of trend lines (insignificant), the others have a negative slope of trend lines (Fig. 3). The highest slope of positive trend lines of IDM, IP, and AI indices is between (0, 0.1), (0, 0.05), and (0, 0.002), respectively. At the same time, the lowest slope of negative trend lines is between (−0.5, −0.4), (−0.25, −0.2), and (−0.016, −0.014). Among the stations that have experienced the highest amount of drying, for IDM index, Sarcheshmeh station with a slope of 0.45. For Janevareh station, IP and AI indices with a slope of 0.22 and 0.015, respectively, have tended toward drying more than other stations. Among the stations that tend to become wetter more than others, the IP of Ghaleh ji station with a slope of 0.025 and IDM and AI indices of Palangan with a slope of 0.045 and 0.0004, respectively, have become wetter than the other stations.

Fig. 3
figure 3

Box plot diagram for the slope of trend lines

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The distribution of the seasonal IDM for the sample station (Hosseinabad) in the different seasons is shown in Fig. 4. Four types of climate can be found on the seasonal scale. The summer is arid by climate, and it has an average value of 0.4. Spring is semi-arid (25.55), autumn is Mediterranean (45.24), while the winter is extremely humid (111.51) for the Sirvan river basin.

Fig. 4
figure 4

Seasonal values of the De Martonne aridity index for the sample station (Hosseinabad)

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The spatial distribution of the seasonal IDM is shown in Fig. 5a–d. In the winter, parts of the basin including Zarivar lake, Janevareh, Ghaleh ji, Kalji, Pirkhezran, Sarcheshmeh, and Negal stations have extremely humid climates, and Palangan, Hosseinabad, and Sarabqamish stations have a very humid condition. During spring, at the west part of the Sirvan river basin, Sarcheshmeh, Zarivar lake, Janevareh, Negal, Kalji, Pirkhezran, and Ghaleh ji stations are in the Mediterranean climate, and the stations of Sarabqamish, Hosseinabad, and Palangan are dominated in semi-arid climates. In summer, with decreasing precipitation and increasing air temperature, dry climatic conditions prevail throughout the basin. However, in autumn, by starting precipitations, Janevareh, Sarcheshmeh, Pirkhezran, Ghaleh ji, and Negal are semi-humid. Mediterranean conditions have been observed in Sarabqamish, Hosseinabad, and Palangan stations. The results of Radaković et al. (2018) showed that in Serbia winters are very humid, spring and autumn are humid, and summers are semi-humid.

Fig. 5
figure 5

Spatial distribution of IDM per season

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The spatial distribution of the annual IDM, IP, and AI index values in the Sirvan river basin is shown in Fig. 6. The stations of Zarivar lake, Pirkhezran, and Ghaleh ji have IDM 28–35, which means that the climate is humid, while the stations of Hosseinabad, Sarabqamish, and Palangan stations have IDM 14–20, which means that the large part of the basin is semi-arid. Mediterranean climate is in the stations of Negal and Pirkhezran, while semi-humid conditions are in the Sarcheshmeh and Janevareh stations. According to IDM classification, about 51.95% of the area of the Sirvan river basin is semi-arid, 13.81% is a Mediterranean climate, 15.52% is semi-humid, and 18.71% is humid climate. Figure 6b shows the zoning based on the IP in the area of the Sirvan river basin. As can be seen from the figure, Sarabqamish, Hosseinabad, and Palangan stations are in dry climates, and Sarcheshmeh, Janevareh, Zarivar lake, Kalji, Pirkhezran, Ghaleh ji, and Negal stations are in a semi-arid climate. Also, according to the IP classification, 50.34% of the basin area is dry and 49.65% has a semi-arid climate. Figure 6c also shows the zoning of AI values in the studied basin. Regarding this figure, Hosseinabad, Sarabqamish, and Palangan stations have AI values of 0.4–0.5, and this value shows the semi-arid climate of the basin, and Negal, Kalji, and Pirkhezran stations have semi-humid climate. At the other stations, the AI values are greater than 0.65, indicating a humid climate in these areas. According to the AI classification, 37.03% of the basin area is semi-arid, 28.19% is semi-humid, and 34.76% has a humid climate. The results of Tabari et al. (2014) showed that about 60% of Iran was arid, 28% semi-arid, 4% Mediterranean, 1% semi-arid, 2% wet, and 5% very wet. The results of zoning for drought indicators revealed that the eastern regions of the Sirvan river basin are drier because the eastern part of the region has a lower altitude and receives less rainfall. Also, the western parts are more affected by the western winds, which discharge the moisture in the western part when the wind blows to the region, and when it reaches the eastern parts, it no longer has moisture. AI shows that the western Sirvan river basin has somehow higher humidity, and the same is showed by the annual IDM and IP.

Fig. 6
figure 6

(a) Annual De Martonne, (b) Pinna combinative, and (c) UNEP index for Sirvan river basin

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Annual values of IDM are given in Fig. 7. From 17 years that analyzed, 5 years are characterized as semi-arid, 1 as humid, and 11 as Mediterranean condition. The average IDM for the Sirvan river basin is 22.5 which means that the climate is Mediterranean. The minimum value of the annual IDM was observed in 2008. The maximum value of IDM was registered in 2016. The IP is analyzed on an annual basis that showed in Fig. 8. From 17 years that analyzed, 1 year is characterized as arid and 16 years are as semi-arid. The average Ip for the Sirvan river basin is 17 which means that the climate is semi-arid. The minimum value of the annual IP was observed in 2008. The maximum value of Ip was registered in 2016. AI is analyzed on an annual basis that presented in Fig. 9. Although IDM, IP, and AI indices are not the same but show similar behavior. According to the AI, from 17 years that analyzed, 5 years are as semi-humid, 1 year is as semi-arid, and 16 years are as humid. The average AI for the Sirvan river basin is 0.76 which means that the climate is humid. The minimum value of the annual AI was observed in 2008. The maximum value of the AI was registered in 2016.

Fig. 7
figure 7

Annual De Martonne aridity index trend for Sirvan river basin

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Fig. 8
figure 8

Annual Pinna aridity index trend for Sirvan river basin

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Fig. 9
figure 9

Annual UNEP aridity index trend for Sirvan river basin

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Figure 10 shows a distribution diagram of points related to the ordered pairs of weighted mean (by using the Thiessen method) for IDM, IP, and AI indices (on an annual scale). As shown in this graph, the points are located around the regression line and less scattered. The coefficient of determination between IDM–IP, IDM–AI, and IP–AI indices is more than 0.98. Therefore, it can be concluded that there is a strong linear correlation between the mentioned indicators in the selected stations of the Sirvan river basin. It is following the results of Baltas (2007), who pointed out that in northern Greece, the correlation between IDM and IP indices was 0.88.

Fig. 10
figure 10

The correlation between De Martonne index (IDM), Pinna index (Ip), and UNEP index (AI)

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Table 5 shows the results of the seasonal IDM trend using the MK method. On a seasonal scale, in autumn, none of the studied stations are statistically significant at any level. In winter, from 10 stations of the IDM coefficient series, one station had a significant downward trend (5%), and the other stations had a downward trend but were not statistically significant. Hosseinabad station with (Z = −2.18) had the highest significant downward trend in winter. In spring, none of the studied stations are statistically significant at any level. In summer, only Zarivar lake station (Z = −1.86) had a significant downward trend at the level of 10%, and other stations had a negative trend but are not statistically significant at any level. According to Table 5, in spring and winter, Hosseinabad and Zarivar lake stations have a significant downward trend.

Table 5 The values of the Z statistic Mann–Kendall for the seasonal De Martonne index
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Figure 11 shows the zonation of the slope value of trend lines (β) in the Sirvan river basin. As can be deduced from this figure, areas with blue and dark blue colors have a slight slope of trend lines, and areas with red and orange colors have a steep slope of trend lines. Figure 11a shows the slope of the IDM trend line. According to Fig. 11a, the area of regions has the values of the slope of trend lines between −0.23 and −0.2, −0.2 and −0.17, −0.17 and −0.14, and −0.14 and −0.11 are equal to 4.55%, 13.78%, 77.5%, and 4.16%, respectively. In Fig. 11b, the area of regions has the values of the slope of trend lines between −0.11 and −0.095, −0.095 and −0.08, and −0.08 and −0.047 are equal to 4.89%, 13.05%, and 82.05%, respectively. Also, Fig. 11c shows the zoning of the slope values resulting from the trend line of the AI. The area of regions has the values of the slope of trend lines between −0.008 and −0.007, −0.007 and −0.006, −0.006 and −0.005, and −0.005 and −0.004 are equal to 4.55%, 16.05%, 75.22%, and 4.16%, respectively.

Fig. 11
figure 11

Spatial distribution of the slope value of trend lines (β) in Sirvan river basin

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Figure 12 shows variations in the percentage of IDM, IP, and AI indices in the Sirvan river basin. From Fig. 12a, the average value of the IDM in different areas of the basin has decreased between −18.67 and −8.71%. The highest percentage of the reduction according to Fig. 12a has been observed around Hosseinabad and Sarabqamish stations. Figure 12a shows zoning percentage reduction of IDM changes. This percentage for the regions that have the values of decreased between −18.67 and −16.18, −16.18 and −13.69, −13.69 and −11.2, and −11.2 and −8.71% are equal to 4.11%, 4.21%, 77.5%, and 4.16%, respectively. Regarding Fig. 12b, the average value of the IP in different areas of the basin has decreased between −17.61 and −7.26%. The highest percentage of reduction according to Fig. 12b has been obtained around Hosseinabad, Sarabqamish, Sarcheshmeh, Janevareh, Kalji, Pirkhezran, and Negal stations. The variations percentage of IP for the regions that have the values of decreased between −17.61 and −15.02, −15.02 and −12.43, and −12.43 and −7.26 are equal to 5.92%, 84.3%, and 9.77%, respectively. The highest percentage of reduction according to Fig. 12c has been occurred around Hosseinabad and Sarabqamish stations. The variations percentage of AI is shown in Fig. 12c. The variations percentage of AI index for the regions that have the values of decreased between −21.22 and −18.78, −18.76 and −16.29, 16.29 and −13.83, and −13.83 and −11.36 are equal to 3.08%, 15.25%, 77.5%, and 4.16%, respectively.

Fig. 12
figure 12

Spatial distribution of variations percentage (a) De Martonne, (b) Pinna, and (c) UNEP indices in Sirvan river basin

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Conclusion

Spatiotemporal analysis of aridity indices by using the nonparametric methods was investigated for the period of 17 years in the Sirvan river basin. The dataset including MMT and MMP is used for calculating seasonal and annual IDM, AI, and IP. Using ArcGIS software, the weighted mean (utilizing the Thiessen method) of the indices was obtained for the whole basin in each year; then the variations trend in each one was calculated by the nonparametric MK method, and the slope of trend lines was calculated by Sen’s slope estimator method. The changes percentage in the amount of indicators were obtained during the studied period for each station. The results showed that IP, IDM, and AI indices revealed the drought and semi-arid climate in large parts of the basin. The results of the seasonal IDM showed that the climate of the basin in the Sarcheshmeh, Hosseinabad, and Palangan stations was humid and in other stations was very humid in winter; in spring in the Sarcheshmeh, Hosseinabad, and Palangan stations, the climate of the basin was semi-arid, and in other stations was Mediterranean. The climate of the basin in the summer was arid, and in autumn, it was semi-humid.

On a seasonal scale in winter, of the IDM drought coefficient series, one station had a significant downward trend at the level of 5%, and the Hosseinabad station with (Z = −2.18) had the highest significant downward trend in winter. None of the studied stations are statistically significant in spring at any level. In summer, only Zarivar lake station (Z = −1.86) had a significant downward trend at the level of 10%. In winter and spring, two stations, Zarivar lake and Hosseinabad, had a significant downward trend at the level of 5% and 10%, respectively. In other seasons, none of the stations were statistically significant at any level. In the annual IDM method, all of the studied stations have a negative Z statistic value, and the Janevareh station was statistically significant at the level of 10%. In the IP method, 5 stations from 10 studied stations have a negative Z statistic value, and the Janevareh station was statistically significant at the level of 10%. Also, in the AI method, 9 stations from 10 studied stations have a negative Z statistic value, and the Janevareh station was statistically significant at the level of 10%. The result of the slope of trend lines showed that more than 75% of stations have a negative slope of trend lines. According to the average of the annual IDM in the studied period, 51.95%, 13.81%, 15.52%, and 18.71% of the basin area has a semi-arid, Mediterranean, semi-humid, and humid climate, respectively. The results of IP climatic classification showed that 50.34% and 49.65% of the basin’s area was arid and semi-arid, respectively. In the classification based on the AI, 37.03%, 28.19%, and 34% of the basin’s area was semi-arid, semi-humid, and humid, respectively.

Based on the above results, it can be stated that the IDM coefficient in most stations has a significant downward trend in cold seasons such as winter, which indicates that the stations in the Sirvan river basin are getting warm and dried. The IP and AI indices showed almost the same results. Therefore, reasonable use of available water is essential, especially in agriculture and horticulture, in which a significant portion of the basin water is used.