1 Introduction

Trend analysis and projections of precipitation, on both the regional and global scales, have attracted attention among climatologists and governments who would come up with more accurate plans using the results. Such plans, particularly in arid and semi-arid regions such as Iran, could benefit hugely from these results.

Iranian economic and industrial progress has taken a faster pace in the last five decades. Fuels such as oil, natural gas and coal have been used in greater amounts. Accordingly, emission of CO2 and other greenhouse gases has been on the rise. Such trends can lead to an increase in temperature and changes in precipitation patterns and the hydrologic cycle. In addition, population growth since the 1970s has put further pressure on land use, agricultural enterprises, livestock farming and solid/liquid waste generation, all of which are responsible for environmental concerns such as climate change (Amiri and Eslamian 2010).

In Iran, the Alborz Mountains area receive the highest amount of precipitation for which several dams have been constructed to store water for agriculture and drinking purposes during summers. Local industries are dependent on farming and husbandry with 65% of the population engaged in related professions. It implies that agriculture and husbandry are directly affected by changes in precipitation pattern. In addition, the area of Hyrcanian forests covering the Alborz Mountain ranges is subject to decline in response to the changes in precipitation patterns. Previous studies show an increasing temperature trend in Asia which will continue in the twenty-first century. However, specifying a uniform precipitation pattern for Asia is not straightforward, because of unreliable and short data as well as different outputs of projection models (IPCC 2014). This shows the importance of precipitation analysis for this region for better management of water resources. Recent droughts have negatively affected Iran’s economy. Therefore, studying the precipitation changes in the past decades and developing a prediction model for the twenty-first century is highly rewarding research topics for Iranian climatologists.

Trend analysis and projections of precipitation series on the global as well as the regional scales have been investigated by many researchers throughout the world. Reviews can be found in Liu et al. (2012), Ramos et al. (2012), Ay and Kisi (2015), Sharmila et al. (2015), Palomino-Lemus et al. (2015), Jiang et al. (2015), Zhao et al. (2015), Eccel and Tomozeiu (2015), Palizdan et al. (2016) and Hu et al. (2016). Chen et al. (2011) highlighted a general increasing trend in annual precipitation in the arid region of Central Asia from 1930 to 2009. Terink et al. (2013) found that annual precipitation will decrease for the majority of the Middle East and Northern Africa region for the periods 2020–2030 and 2040–2050, with the decreases of 15–20% for the latter period. Deng et al. (2013) used nine CMIP5 datasets under different RCPs scenarios for the projections of spring and summer precipitation for the period 2013–2050 over the Yangtze River basin, China. The precipitation projections show significant positive linear trends of spring precipitation under the RCP2.6 and RCP8.5 scenarios, whereas summer precipitation will mainly undergo an inter-annual change. Yao and Chen (2015) reported a significant rising trend at a rate of 4.44 mm/decade and step change points in 1991 in annual precipitation for the Syr Darya basin during 1881–2011. Meshram et al. (2016) used MK test, Spearman’s rho and Sen’s slope estimator to identify precipitation trends in Chhattisgarh State, India. Results showed a significant decreasing trend at the 5% significance level in annual precipitation at most of the stations according to these tests. Chandniha et al. (2016) applied MK test, Sen’s slope estimator and Mann–Whitney tests for trend detection in annual precipitation at 18 meteorological stations in Jharkhand State, India. The result showed a decreasing trend in annual precipitation at 5 out of 18 stations during the whole period.

Iran, with an area of 1,648,000 km2, is located in the southwest of the Middle East which is situated in the mid-latitude belt of arid and semi-arid regions. The climate of Iran is arid or semi-arid except the coastal areas of the Caspian Sea and the foothill of the Alborz and Zagros Mountains. The average amount of precipitation over the country is 252 mm/year, which is less than one-third of the world average (Alizadeh and Keshavarz 2005). Precipitation in Iran has a high spatial and time variability. There are regions in the south of the Caspian Sea and some parts of the Zagros Mountains area which receive annual precipitation between 1200 and 2000 mm, whereas portions of the central part of Iran and Dasht-e Loot get less than 50 mm (Shifteh Some’e et al. 2012). Most of the precipitation falls during the winter and autumn seasons, due to the prevalence of humid westerly winds of the Mediterranean Sea.

Delju et al. (2013) applied statistical techniques to detect trends in precipitation series. The results indicated that mean precipitation increased at the rate of 9.2% from 1966 to 2005 over the Urmia Lake basin in the northwest of Iran. Zarenistanak et al. (2014a) reported insignificant trends in annual and seasonal precipitation series at most of the stations located in the southwest of Iran. Arbabi Sabzevari et al. (2015) concluded no long-term trends in annual and monthly precipitation series in the southwestern Iran. Feizi et al. (2014) applied MK test for trend detection in precipitation series over Iran from 1969 to 2008. The results indicated that precipitation during summer and autumn had a negative trend in the southeastern parts of Iran which was stronger than the trend in spring, but no significant trend was detected in winter. Farhangi et al. (2016) revealed a decreasing trend in mean annual precipitation series at six out of ten stations located in western Iran. The temporal changes in precipitation and other climatic variables in Iran have also been found in several studies (e.g., Rahimzadeh et al. 2009; Sheikha and Bahremanda 2011; Dinpashoh et al. 2011; Tabari et al. 2011; Kousari et al. 2011; Tabari et al. 2012a; Tabari and Aghajanloo 2013; Tabari et al. 2014; Abghari et al. 2013; Zarenistanak et al. 2015).

Climate models could be useful tools to project climate variables. The World Climate Research Program Coupled Model Intercomparison Project not only provides a foundation for research groups to develop their Earth system models, but also contains more than 20 model datasets. CMIP has motivated using numerous researchers to project global and regional climate changes (Deng et al. 2013). The projection of precipitation changes in the Alborz Mountains has not received considerable attention from the government. In this paper, precipitation projections in the Alborz Mountains area during the twenty-first century by three models under the RCP4.5 and RCP8.5 scenarios are analyzed. A number of papers have reported regional climate change simulations over some part or the whole extent of Iran. Jafari (2012) highlighted a future winter precipitation increase of 10% and a summer precipitation decrease of 20% in the west of Gilan Province in the north of Iran under the A1B scenario from 2090 to 2099. Roshan and Grab (2012) used MAGICC/SCENGEN 5.3 compound model for precipitation projection over Iran. The results revealed that by the year 2100, the mean precipitation may increase by 36% relative to the period 1961–1990. Dhorde et al. (2014) found insignificant trends in annual and seasonal precipitation series over the southwest of Iran. The highest numbers of stations with significant trends occurred in winter. Results for the future projections showed that precipitation may decrease according to the majority of the models under the B1 and A1B scenarios, but the magnitude of this decrease may not be large, except for the MIROCH model by 2100. Babaeiana et al. (2015) used PRECIS regional climate model for precipitation projection over Iran. Results showed a decrease in mean annual precipitation toward the end of the twenty-first century by 7.8 mm in the B2 scenario and 10.1 mm in the A2 scenario, with a maximum regional decrease of 100 mm in the southeast of the Caspian Sea. Nazemosadat et al. (2016) reported that under the 20C3M scenario, precipitation may decrease by about 20% in the southern part of Iran in comparison to the historical time series.

Previous studies carried out in Iran only focused on precipitation trend analysis or projections. In this study, several statistical tests were used for trend detection in precipitation series and also three models under two scenarios were applied for precipitation projections to find out how global warming impacts the precipitation of the study area. This study focused on two main objectives. The first one was to detect the trends in the annual and seasonal precipitation over the Alborz Mountains area using the linear regression, the MK test, the SQ-MK test and the Sen’s slope estimator for the period 1950–2014. The second one is to project precipitation using GFDL-CM3, HadGEM2-AO and MPI-ESM-MR models under the RCP4.5 and RCP8.5 emissions scenarios over the study area.

2 Methodology

2.1 Study area and data

The Alborz Mountains area covers the northern part of Iran, particularly the provinces of East Azerbaijan, Ardabil, Zanjan, Qazvin, Tehran, Gilan, Mazandaran, Semnan and Golestan. The study area is located between 35°52′N and 39°26′N latitude, and 45°7′E and 56°3′E longitude. Having an approximate area of 207,221 km2, it covers about 14% of the country land area (Fig. 1). The elevation ranges from − 20 m in the coastal areas of the Caspian Sea to over 5671 m in Damavand Mountain. Damavand Mountain as the highest mountain in Iran is located in the central Alborz Mountain range. These mountains avoid the Caspian Sea moisture-bearing systems by crossing through the central region of Iran. In these mountains, several rivers originate. The rivers are generally fed by the snow accumulated in the mountains and the rainfall in the wet season. Generally, these rivers in this area can be divided into two categories. The rivers in the north foothill, such as Chalus River, Do Hezar River, Sardab River, Kojur River, Haraz River, Atrek River and Aras River, empty into the Caspian Sea. The second category is the rivers in the south Alborz Mountain foothill, of which the Alamut River, Shahrud River, Jajrood River and Lar River are the most important ones. The rivers from the latter category flow to the central part of Iran.

Fig. 1
figure 1

Geographic location of the study area and spatial distribution of the rain gauge stations

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The north foothill of the Alborz Mountains is covered with the Hyrcanian forests. The forests cover about 55 km2 of the southern shores of the Caspian Sea and Azerbaijan region. The economy of the region depends on fishing, industrial activities, agriculture, horticulture and animal husbandry. The region is a large producer of rice, grain and fruits. Most of the irrigation waters in the region are provided by precipitation.

For the period between 1950 and 2014, the precipitation data of 154 stations provided by the Islamic Republic of Iran Meteorological Organization (IRIMO) and Iranian Water Resources Management Organization were used for statistical analysis. The details of data availability for these 154 stations are reported in Table 1. The precipitation data were carefully checked for homogeneity and missing values. Missing values were estimated based on correlation analysis between the investigation station and the nearest station in its neighborhood. Homogeneity of the data was evaluated by the Pettitt’s (Pettitt 1979) and Buishand range (Buishand 1982), the standard normal homogeneity (Alexandersson 1986) and the standard normal homogeneity by Alexandersson and Moberg (Alexandersson and Moberg 1997) tests. Thus, the homogeneity of the annual and seasonal precipitation series analyzed in this study has not been affected.

Table 1 Geographic characteristics of the rain gauge stations used in the study
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2.2 Precipitation characteristics

The Alborz Mountains area receives the highest amount of precipitation in Iran. The seasonal distribution of precipitation in this area is as follows: during autumn, the southwestern coasts of the Caspian Sea receive heavy precipitation thanks to winds coming from Siberia that create advectional processes. In spring, the heights in the Azerbaijan region receive more precipitation due to foothill convections. During winter, there is relatively good precipitation in the whole area, thanks to western winds and humidity of the Mediterranean and Caspian seas. Winter precipitation is mainly snow, lasting some 3–5 months in the mountainous areas and 2–3 months on the coast of the Caspian Sea. The decreasing pattern of precipitation toward the Alborz heights shows that annual perspiration decreases from the coasts to the northern Alborz heights, although on the southern side it decreases toward the lower lands. The eastern coasts of the Caspian Sea receive humid flows carried by western currents coming from the Gorgan valley into the east. Accordingly, the precipitation gradually decreases toward the east. This trend is accelerated to the point of sudden in toward the south and west, thanks to the Alborz Mountains. In the southwestern coasts, the maximum spots lie in seashores and inland in western coasts. This happens due to the presence of the impact of Siberian currents and sunlight. Precipitation variability over the Caspian Sea coasts is significantly influenced by the EL Niño-Southern Oscillation (ENSO) phases, the sea surface temperature (SST) and the intensity of the Siberian high (Nazemosadat and Ghasemi 2004; Nazemosadat 2001). The windward slops of the Azerbaijan mountains receive more precipitation than the lower altitudes and the lee slopes (Alijani 1995).

2.3 Statistical tests for trend analysis

The statistical techniques used in the research are linear regression, MK test, SQ-MK test and Sen’s slope estimator. The significance testing for all tests was performed at a 95% confidence level. These tests have been applied by many researchers for detection of the statistical significance of the trends in the climatological time series (e.g., Schlunzen et al. 2010; Tabari and Hosseinzadeh Talaee 2011b; Yavuz and Erdoğan 2012; Tabari et al. 2012b, 2016; Martinez et al. 2012; Hanif et al. 2013; Scardilli et al. 2015). A brief explanation of these statistical methods is presented in the subsequent sections.

2.3.1 Linear regression

In this study, the magnitude of the trends was derived from the slope (value of ‘b’) of the regression line. The value of ‘b’, which represents the rate of change per year for the climatic variable under consideration, was multiplied by 10 to obtain the decadal change. The trends detected by the regression method were then tested for statistical significance by employing t test. Finally, the results obtained from the linear regression analysis were compared with those from the MK test and Sen’s slope estimator.

2.3.2 Mann–Kendall rank test (MK test)

Detection of significant trends in climatic and hydrological time series is mostly facilitated by using the non-parametric MK test, which is one of the most popular trend tests. In this test, the relative values of the terms in the series Xi are used. Accordingly, the first step has to do with replacing the Xi values by relevant ranks ki. To do so, a number (1 to N) is initially attributed to each value, and then the statistic value P is obtained as follows:

  • The rank of the first value (k1) is weighed against the ranks of the later values (from 2nd to the Nth).

  • The number of later values with the rank exceeding ki is found. The number is shown by n1.

  • The rank of the second value (k2) is weighed against the ranks of the later values and the number of later values with the rank exceeding ki is obtained. This number is denoted by n1.

These directions are applied for each value of the time series till kN−1 and its corresponding number nN−1.

Using the following equation, P can be computed:

$$P = \sum\limits_{I = 1}^{N - 1} {n_{i} } .$$
(1)

The next step involves computation of τ:

$$\tau = \frac{4P}{N(N - 1)} - 1.$$
(2)

The value of the τ is translated into the basis of a significance test through comparing it with:

$$\tau = 0 \pm t_{g} \sqrt {\frac{4N + 10}{9N(N - 1)}} ,$$
(3)

where tg represents the desired probability point in terms of Gaussian normal distribution. In the present study, tg at the 0.05 point was chosen for comparison.

2.3.3 Sequential Mann–Kendall test (SQ-MK test)

The present study used the non-parametric SQ-MK test (Sneyers 1990) to specify the change point or the approximate beginning year in significant trends. The test includes two series: progressive series u(t) and backward series u′(t). If these series intersect, and then set apart and exceed certain threshold values (± 1.96 for the 95% confidence level), a statistically significant trend exists. Thus, u(t) should be seen as a standardized variable with zero mean and unit standard deviation and its sequential behavior revolves around the zero level. u(t) equals the values which appear in the first data point up until the last. In other words, the SQ-MK test takes into account the relative values of all terms in the time series (x1,x2,…, xn). The test statistic is computed as follows:

  • xj annual mean time series (j = 1,…, n) are evaluated with regard to xk, (k = 1,…, j − 1) and the number of cases where xj  >  xk are counted for each comparison and is designated by nj.

  • The test statistic is then calculated as:

    $$t_{j} = \sum\limits_{1}^{j} {n_{j} } .$$
    (4)

    The mean and variance are determined by:

    $$e(t) = \frac{n(n - 1)}{4},$$
    (5)
    $$\text{var} \;t_{j} = \frac{j(j - 1)(2j + 5)}{72}.$$
    (6)

  • Finally, the sequential values of u(t) are calculated using the following equation:

    $$u(t) = \frac{{t_{j} - e_{(t)} }}{{\sqrt {\text{var} (t_{j} )} }}.$$
    (7)

In a similar procedure to u(t), u′(t) values are reversely calculated, starting from the end of the series. The sequential version of the MK test is an effective method to specify the beginning year of a trend. The crossing point of the forward and backward curves shows the time when a trend or change begins.

2.3.4 Sen’s slope estimator

The Sen’s slope estimator method was employed to specify the magnitude of the long-term trends in precipitation. With a linear trend in time series, the slope (change per unit time) can be determined by using a simple non-parametric procedure first suggested by Sen (1968). Recently, the Sen’s slope estimator method has taken precedence over a linear regression for estimating trend slope in meteorological and hydrological studies.

The method can be expressed mathematically as follows. First, the Sen’s slope values within N pairs of data are calculated:

$$Q_{i} = \frac{{x_{j} - x_{k} }}{j - k}\quad \quad \quad {\text{for}}\;i = 1, \ldots N,$$
(8)

where xj and xk represent data values at times j and k (j  >  k), respectively. Sen’s estimator of slope is simply the median of these N values of Qi. Wherever N is an odd number, the Sen’s estimator is obtained by:

$$Q_{\text{med}} = Q_{(N + 1)/2} .$$
(9)

Wherever N is an even number, the Sen’s estimator is obtained by (Partal and Kahya 2006):

$$Q_{\text{med}} = \frac{1}{2}Q_{{\left[ {N/2} \right]}} + Q_{{\left[ {\left( {N + 2} \right)/2} \right]}} .$$
(10)

To figure out the sum of all changes over the study period, the calculated slope can be multiplied by the number of years (here multiplied by 10 to get the decadal change).

2.3.5 Eliminating serial correlation

Prior to the statistical analysis of precipitation series, the pre-whitened test is applied to omit correlation among the series (von Storch 1995). In fact, the serial correlation significantly bears on trend detection methods (e.g., MK test) and their results. Accordingly, many recent studies have employed pre-whitened method to deal with serial correlation in meteorological parameters (e.g., Xu et al. 2010; Tabari and Hosseinzadeh Talaee 2011b; Masih et al. 2011; Zarenistanak et al. 2014b; Abghari et al. 2013; Arbabi Sabzevari et al. 2015).

The following steps are taken to identify possible statistically significant trends in the precipitation series (x1, x2, x3,… xn).

Step 1 :

Find lag-1 serial correlation coefficient (represented by r1)

Step 2 :

If r1 is not significant at the 5% level, the original data of the time series must be tested

Step 3 :

If the calculated r1 is significant, first the pre-whitened test is performed rather than statistical tests. Pre-whitened test is performed via this formula: (x2 − r1x1, x3 − r1x2,… xn − r1xn − 1) (Partal and Kahya 2006).

2.3.6 Coefficient of variation (CV)

To understand the variability in precipitation, CV, a statistical measure of the dispersion of data points in a data series around the mean was calculated by the following formula:

$${\text{Coefficient of variation}} = \frac{S}{{\overline{x} }}*100,$$
(11)

where \(\overline{x}\) is the average of rain gauge stations and S is the standard deviation for each station. In other words, the coefficient of variation represents the ratio of the standard deviation to the mean and is a useful tool for comparing the degree of variation from one data series to another, even if the means are drastically different from each other.

2.4 Model description

In this study, the outputs from three GCMs were used under two scenarios (i.e., RCP4.5 and RCP8.5) for precipitation projections in the north of Iran. The coupled climate models, whose data were available, are listed with key references in Table 2. Using Gordess and Matlab software, data points were extracted from global data, while the GIS application was employed to locate the coordinates. Afterward, a mean value of the points was processed and utilized. The historical simulations were integrated from 1980 to 2000, and the projections for both RCP4.5 and RCP8.5 were analyzed from 2000 to 2100. RCP4.5 is a stabilization scenario in which the total radiative forcing is stabilized before 2100, without overshooting. It uses a range of new technologies and strategies for reducing greenhouse gas emissions (GHGs). RCP4.5 and RCP8.5 indicate a concentration pathway that results in a radiative forcing of ∼ 4.5 and ∼ 8.5 W m−2 in 2010, respectively. RCP 8.5 is characterized by increasing GHGs over time, which leads to higher GHG concentrations and is related to preindustrial conditions (Taylor et al. 2009; Wei and Bao 2012).

Table 2 Climate models and their key references participating in the CMIP5
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3 Results and discussion

3.1 Trend analysis

Annual and seasonal precipitation and CV zones for the period 1950–2014 are depicted in Figs. 2 and 3, respectively. The mean annual precipitation for the study period was 440 mm. Ten stations from the west of the Caspian Sea coasts received annual precipitation more than 1000 mm. The mean average seasonal precipitation from 1950 to 2014 were 136, 131, 51 and 126 mm in winter, spring, summer and autumn, respectively. CV was computed for all stations to investigate the spatial pattern of precipitation variability over the study area. In annual CV zones, most of the stations located in the east of the study area indicated the largest CV values where the precipitation amount was low (Fig. 3). In addition, the winter and summer seasons showed the lowest and highest CV, respectively. The average CV for annual precipitation is 33%, for winter 32%, for spring 47%, for summer 105% and for autumn 51%.

Fig. 2
figure 2

Annual and seasonal precipitation zones

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Fig. 3
figure 3

Spatial pattern of coefficient of variation of annual and seasonal precipitation zones

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A preliminary analysis showed that the majority of the precipitation time series had no significant lag-1 serial correlation coefficient (Table 3). The highest number of significant serial correlation was observed in the annual series.

Table 3 Results of the significant lag-1 serial correlation coefficient for annual and seasonal precipitation series
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Figure 4 shows the percentage of stations with significant trends in the annual and seasonal precipitation time series for the period 1950–2014. Both positive and negative trends were identified by the linear regression, the MK test, the SQ-MK test and the Sen’s slope estimator in the annual and seasonal precipitation series. Nevertheless, most of the trends were insignificant at the 95% confidence level. Based on the results of the linear regression analysis, spatial distribution maps for precipitation significant changes (in mm/decade) were prepared as presented in Fig. 5. In the annual precipitation series, on average 11% of the stations showed a significant positive trend and 20% showed a significant negative trend. Spatial distribution of annual precipitation trends showed negative tendencies in the central parts of the study area with rates ranging between − 20 and − 100 mm/decade (Fig. 5). Five stations showed a significant positive trend for annual precipitation with rates ranging between 40 and 60 mm/decade. Shifteh Some’e et al. (2012) reported that over the 1950–2006 period, a negative trend in annual precipitation occurred at 79% of Iranian stations, while only three stations had a significant negative trend at the 95% confidence level. In addition, Tabari et al. (2011) found insignificant negative trends in the annual precipitation series at the majority of the Iranian stations.

Fig. 4
figure 4

Percentage of stations with significant trends at the 95% confidence level by linear regression, SQ-MK test, MK test and Sen’s slope estimator for annual and seasonal precipitation series

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Fig. 5
figure 5

Significant trends (mm/decade) in annual and seasonal precipitation

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For all the selected stations, the linear regression analysis, the MK test, the SQ-MK test and the Sen’s slope estimator were also applied to detect the trends of the seasonal precipitation time series during 1950–2014 (Figs. 4, 5). As shown in Fig. 4, the majority of the trends in the seasonal series occurred in winter (negative) and summer (positive). Based on the results of the statistical tests, the significant negative trends in the winter precipitation series were found at 35% of the stations (Fig. 4). 21 stations with significant negative trends are located in the west and central parts of the study area with a trend magnitude ranging between − 20 and − 100 mm/decade (Fig. 5). The stations with the altitudes higher than 1500 m show significant negative trends during winter, especially in case of the Central Alborz Range (Fig. 5). A review of the data revealed that snowfall amount was decreased, probably due to less snow cover which itself invites further studies. Five stations revealed a significant positive trend during winter with a slope range between 6 and 57 mm/decade. Spring precipitation mainly decreased in the western parts of the study area characterized by six stations. Significant positive trends were found only at Vatana and Lowshan stations with rates of 30 and 15 mm/decade, respectively. Summer precipitation increased more during the study period as compared to the other seasons. The results of linear regression analysis, MK test and Sen’s slope estimator showed 47, 60 and 56% of the stations having a significant positive trend with increasing trend rates of 5 and 40 mm/decade, respectively. The precipitation systems that move to Iran via the Mediterranean Sea are stopped or diminished during summer, mainly because of the presence of the subtropical high, giving way to the regional precipitation systems. During this season, most of the rain gauge stations installed in the Central Alborz Range and also in the foothills facing the Caspian Sea coasts indicate significant positive trends (22 stations). Mountains and heights in the Central Alborz Range are close to the sea, allowing increasingly humidity entrance to the region, while temperature and vaporization escalate, leading to the emergence of convectional rainfalls. Mir Kuh, Harawi, Bostanabad, Sahzab and Sultanate stations situated in the western parts of the study area show significant positive trends, a fact explained by regional factors especially topographic features. These stations lie in valleys that carry humidity from the Caspian Sea. Sqanfar Qur’an and Ammameh-e in the east of the study area, located at the bottom of foothills against the sea, showed significant negative trends with rates of − 28 and − 42 mm/decade, respectively.

As shown in Fig. 4, autumn precipitation was more stable than the other seasons. Now Deh, Vatana, Soleyman Tangeh, Mohammad Deh and Ammameh-e showed significant positive trends with rates of 27, 52, 13, 8 and 36 mm/decade, respectively. Only Galugah station showed a significant negative trend at the rate of − 31 mm/decade. Hosseinzadeh Talaee (2014) found an insignificant trend in the annual and seasonal rainfall series at the majority of the considered stations over Iran.

It was revealed that those stations with significant positive trends in winter, autumn and spring are mostly either inside or in the vicinity of towns (Now Deh, Vatana, Soleyman Tangeh, Mohammad Deh, Ammameh-e Lowshan). Thanks to urban expansions in Iran, especially since the 1970s, and migration of populations from countryside to cities, urban areas have come to occupy more lands, enveloping the stations that used to lie outside city limits. In fact, the positive rainfall trends are influenced by urban microclimate. It should be noted these speculations are authorial.

Following the SQ-MK test, a graphical analysis using u(t) and u′(t) statistics was performed for the annual and seasonal precipitation series at 154 study stations. In this way, the onset of the change in the time series is detected by pinpointing the intersection point of the curves. The positive or negative trend for each station is also determined by analyzing the plots as well as the point of change in the mutation point. The results of the SQ-MK test for the period 1951–2014 reveal a statistically significant mutation point in the annual and seasonal precipitation time series in the 1970s at most of rain gauge stations (Table 4). All mutation points (either positive or negative) in the autumn series occurred in the 1970s. Similarly, all negative mutation points in the summer series occurred in the 1970s. Following the 1970s, most of the mutation points lie in the 1980s. An illustrative example is shown in Fig. 6, which clearly demonstrates a mutation point in 1973 in the total annual precipitation time series of Bastam. These findings are in good agreement with the results of Nazemosadat et al. (2006), who found a significant mutation point in or around the mid-1970s over the northern parts of Iran. He reported that the mid-1970s is the most probable change point year in the time series of the Southern Oscillation Index (SOI) data for the period 1951–1999 over Iran. Consistent with this finding, precipitation data from the northern parts of Iran have also shown significant change years in or around the mid-1970s. Molavi-Arabshahi et al. (2016) revealed that during 1996–2010 precipitation variations over the southwest coast of the Caspian Sea show strong connections with ENSO and weaker ones with NAO (North Atlantic Oscillation). The trends of precipitation during this period are diverse, but display mostly a weak decrease. Besides ENSO, Madden Jullian Oscillation (MJO) also plays a role in Iran in terms of precipitation variability, as suggested by Nazemosadat and GHaed Amini AsadAbadi (2010) and Nazemosadat and Shahgholian (2017).

Table 4 Values from stations recording significant mutation points (in percent)
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Fig. 6
figure 6

Graphical illustration of the series u(t) (solid line) and backward series u′(t) (dashed line) of the SQ-MK test for annual precipitation series observed at Bastam station

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For annual precipitation series of the period 1950–2014, most of the stations under study show insignificant trends, a result very much in line with what previous research has found either in Iran or certain parts of it (e.g., Tabari and Hosseinzadeh Talaee 2011a; Moazed et al. 2012; Shifteh Some’e et al. 2012; Raziei et al. 2014; Khalili et al. 2014). For the seasonal series, winter shows the greatest number of significant negative trend, while summer shows the greatest significant positive trend. This matches the results reported by Shifteh Some’e et al. (2012), who found a decrease in winter precipitation amount for the northern part of Iran. An increasing trend in summer was also noted by Javari (2016) in the west and north of Iran for the period 1975–2014. In addition, Asakereh (2016) found a small increase in summer precipitation in the northwest of Iran.

3.2 Precipitation projections

In this study, precipitation historical (1980–2000) and future (2000–2100) runs of three CMIP5 global climate models (GFDL-CM3, HadGEM2-AO and MPI-ESM-MR) were employed. The projection was based on two representative concentration pathways (RCP4.5 and RCP8.5). Figure 7 depicts a comparison between the observed seasonal precipitation series (mm) and the simulations from each model for the period 1981–2014 to evaluate the accuracy of the model outputs. Based on the observed data, the models can be classified into two categories: GFDL-CM3 and MPI-ESM-MR models underestimated annual precipitation, while HadGEM2-AO model overestimated it.

Fig. 7
figure 7

Average of the observed precipitation and the simulations by the three models from 1980 to 2014

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The range of precipitation changes is presented in Table 5. The precipitation projections do not indicate substantial future precipitation changes except in the summer. Most of the models under both scenarios showed a precipitation decrease by the end of the twenty-first century. Figure 8 shows future projections of annual mean precipitation. The results of the GFDL-CM3 model showed that precipitation may decrease by − 4.7 and − 14.95% under RCP4.5 and RCP8.5, respectively. The results of the HadGEM2-AO model showed that precipitation may increase by 3.5% by 2100 based on the RCP4.5 scenario. However, the projections for the RCP8.5 scenario indicated that precipitation may increase by 5.2% by 2100. The MPI-ESM-MR model projected precipitation decreases of − 12.36 and − 14.05% by 2100 based on the RCP4.5 and RCP8.5 scenarios, respectively. Roshan et al. (2012) reported annual precipitation increases of 25.19 and 26.4% for 2025 and 2050 compared to 2005, respectively. Babaeian et al. (2013) also found that annual mean precipitation over the southeast of the Caspian Sea, in the south of the Zagros Mountains and northwest and southeast provinces of Iran, will decrease by 0.1–0.2 mm/day under the A2 and B2 scenarios compared to 1961–1990.

Table 5 Precipitation changes (%) for the period 1981–2100
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Fig. 8
figure 8

Projections for annual precipitation under the RCP 4.5 and RCP 8.5 scenarios

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The results of seasonal precipitation projections using three models under the RCP4.5 and RCP8.5 scenarios for the periods 1981–2000, 2001–2020, 2021–2040, 2041–2060, 2061–2080 and 2081–2100 are depicted in Figs. 9 and 10, respectively. In the seasonal time series, larger precipitation changes may happen in the summer season under both scenarios. The time series of spring precipitation showed a decrease by all three models under both scenarios (Table 5). As compared with the base period, precipitation may decrease in summer under the RCP8.5 scenario according to all the models. Under the RCP4.5 scenario, precipitation may increase in autumn according to all the models. The precipitation changes for the twenty-first century are not uniform. No clear pattern in precipitation changes is evident during any season, as can be seen in Figs. 9 and 10. This may be due to the complexity in interpreting precipitation projections, since different models often do not agree on whether precipitation will increase or decrease at a specific location and agree even less on the magnitude of that change (Agarwal et al. 2014).

Fig. 9
figure 9

Projections for seasonal precipitation series under the RCP 4.5 scenario

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Fig. 10
figure 10

Projections for seasonal precipitation series under the RCP 8.5 scenario

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Figures 11 and 12 illustrate the changes in annual precipitation between 1981–2000 and 2081–2100 over the study area under both scenarios. Precipitation may increase in the northwest of the study area up to 3.2% as compared to 1981–2000. Precipitation may decrease from the west to the east of the study area under the RCP 4.5 scenario (Fig. 11). The GFDL-CM3 model showed a precipitation decrease in the entire study area under the RCP 8.5 scenario at the rate between − 9 and − 11% (Fig. 12). According to the HadGEM2-AO model, under the RCP4.5 scenario, precipitation may increase in the northwest of the study area, while a decrease was projected for the southeast of the study area as compared to the base period (Fig. 11). Under the RCP8.5 scenario, precipitation may increase in the central part of the study area and decrease in the west and east regions (Fig. 12). The MPI-ESM-MR model, under both scenarios, projected a precipitation decrease, for the whole study area with larger decrease in the central part (Figs. 11 and 12).

Fig. 11
figure 11

Projected annual precipitation changes between the late twentieth century (1981–2000) and the late twenty-first century (2081–2100) under the RCP 4.5 emission scenario

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Fig. 12
figure 12

Projected annual precipitation changes between the late twentieth century (1981–2000) and the late twenty-first century (2081–2100) under the RCP 8.5 emission scenario

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4 Conclusions

In the present study, a statistical trend analysis and projections of annual and seasonal precipitation were performed in the Alborz Mountains area. The linear regression, the MK test, the SQ-MK test and the Sen’s slope estimator were used for trend analysis at 154 stations in the Alborz Mountains area for the period 1950–2014. To evaluate the homogeneity of the precipitation data, the Pettitt’s and Buishand range, the standard normal homogeneity and the standard normal homogeneity by Alexandersson and Moberg tests were applied. Furthermore, pre-whitening approach was applied to eliminate the effect of serial correlation on the MK test. The precipitation projections from 1980 to 2100 were derived from three CMIP5 datasets under the RCP 4.5 and RCP 8.5 scenarios. The results of the homogeneity test showed that the precipitation series were not affected. The results of pre-whitening showed that precipitation data were serially correlated showing the independency of the data. The results of the trend analysis indicated insignificant trends in annual and seasonal precipitation at most of the stations considered. Furthermore, at the seasonal level, the highest number of stations with significant negative trends in precipitation occurred in winter, while positive significant trends were detected in summer precipitation. The results of the SQ-MK test show that most of the significant mutation points in annual and seasonal precipitation series began in the 1970s. The previous research indicated that precipitation variability in the study area significantly influenced by the ENSO phenomenon.

Based on the results, CMIP5 can also simulate the precipitation variability in the Alborz Mountains area during the period 1980–2100. The projected precipitation changes showed that precipitation may decrease according to most of the models under the RCP 4.5 and RCP 8.5 scenarios, but the decrease may not be large except in summer in 2100.

Due to the distance between the spots, their height, and the validity of output, the model precipitation simulations are less reliable in mountainous regions than other areas. However, experts and policy makers can hugely benefit from the results in drawing more accurate plans for water resource management in arid and semi-arid countries such as Iran. Results of climate changes in Iran affect not only precipitation and temperature, but also drought, successive hurricanes, vaporization, humidity and particularly agriculture. Yet, all these repercussions must be taken into account to assess their influence on the economy, environment, water resources and most importantly on food security in the twenty-first century. In this way, policy makers can better prepare for possible negative outcomes that may challenge people’s lives.