1 Introduction

The rise in greenhouse gas emissions arising from increased industrialization and urbanization has, in recent years, contributed significantly to global warming, which has, in turn, led to shifts in global climate parameters (e.g., changes in the quantity, temporal pattern and areal distribution of precipitation, shifts in temperature (Richardson et al. 2011)). The Fifth Report of the Intergovernmental Panel on Climate Change notes that by-and-large all portions of the globe (except a small region in the North Atlantic) have experienced a rise in temperature over the last century (IPCC 2013). Such upward increments in temperature have major effects on losses of water resources, rising crop evapotranspiration as well as many other climatological and hydrological factors which ultimately have an impact on human and ecosystems (Henderson-Sellers and McGuffie 2012; USDA 2013; Dinar and Mendelsohn 2011). The potentially dire consequences of climate change have led, in recent years, to a worldwide upsurge in research in this field. Trend analysis of climatological parameters, especially temperature, is one of the major methods for detecting changes in climate. An analysis of monthly mean temperatures from 473 stations in Spain between 1961 and 2006, showed temperature to have generally increased during all months and seasons of the year over the study period (del Río et al. 2011). Using Mann–Kendall (MK), Sen’s slope, and sequential MK methods to detect trends in air temperature in Romania, Croitoru et al. (2012) showed most of the country to have experienced a positive increase in temperature. Monthly mean temperature in Malta rose by an average of 1.1 °C between 1951 and 2010, with the largest changes occurring during the months of June, August, and October (Galdies 2012). While mean temperatures across India rose by 0.24 °C per decade between 1971 and 2009 (Bapuji Rao et al. 2014), in contrast, at certain locations in the country (e.g., Pune), mean temperature declined significantly between 1901 and 2000 (Gadgil and Dhorde 2005). Near surface temperatures in Armenia increased significantly between 1979 and 2012, surpassing the rate of increase between 1961 and 1994 (Gevorgyan 2014). Applying the MK test to temperature readings from 80 spatially-distributed weather stations in Sicily, Italy, Viola et al. (2014) found there to be a general warming trend in Sicily over the period of 1924 to 2006. Studying temperature parameters for 35 synoptic stations in Iran using an MK test revealed that most of the stations, particularly those in the eastern and western parts of the country showed significant positive trends, especially in the summer (Saboohi et al. 2012). Applying the MK test and wavelet transforms to a high resolution air temperature gridded data file for a period from 1956 to 2010, Araghi et al. (2015) showed that all regions of Iran showed positive temperature trends over this period, and that these were particularly strong in the warmer seasons. Given the effects of extreme temperatures on agriculture, ecosystems, human society, and other biological systems, especially in arid and semi-arid regions prone to water crises, this study analyzed the trend in the number of days with extreme temperatures occurring in Iran over the past five decades. It must be noted that most of the previous studies for temperature trends in Iran have focused on monthly (e.g., average, maximum, or minimum) temperatures (Tabari and Hosseinzadeh Talaee 2011; Tabari and Talaee 2011; Saboohi et al. 2012; Kousari et al. 2013), while this study is focused on extreme daily temperatures with specified criteria (e.g., more than 30 °C and less than 0 °C). These extreme thermal data are very important factors in ecology, agriculture, and also in some hydrological applications and processes. For example, many plants and biological systems are unable to function properly in temperatures of more than 30° to 35° C, while some other plants need under zero temperature periods for their biological growth (Connor et al. 2011). Precipitation type, snow melting rate, topsoil water availability, evapotranspiration, etc. are some of the issues that are strongly affected by extreme daily temperatures (Karamouz et al. 2013).

2 Data and methods

Approximately 1.65 × 106 km2 in area, Iran is situated between 25°N to 38°39′N latitude and 44°E and 63°25′E longitude in south west Asia. Based on the Köppen method, most regions of Iran have an arid to semi-arid climate (Dinpashoh et al. 2011; Ahrens 2011; Saadat et al. 2011). Less than a third of global mean precipitation of 830 mm year−1, the roughly 250 mm year−1 in mean precipitation across Iran shows great spatiotemporal variability (Modarres and de Paulo Rodrigues da Silva 2007; Tabari et al. 2012). It is well-known that as the record length increases, the validity of the results increases accordingly. There are more than 200 synoptic stations in Iran, but most of these stations do not have sufficient data record length. To analyze trends in the number of days with extreme temperatures, daily temperature maxima and minima (T d max, T d min, respectively) between 1961 and 2010 were collected from 30 synoptic meteorological stations (Table 1, Fig. 1) spread across all of Iran and free of data lacunae. The selected stations have the best quality and longest record datasets among all of the synoptic stations in Iran and for this reason, most of the previous studies on climatic variables in this country were focused on these stations as well (Saboohi et al. 2012; Shifteh Some’e et al. 2013; Tabari and Hosseinzadeh Talaee 2011; Tabari et al. 2011b; Tabari and Talaee 2011). In addition, the central part of Iran has a very arid climate with very little precipitation. So these parts of Iran (that are called the Central Desert and Lut Desert) have very little human habitation, and as such there are not many synoptic stations in the central parts of the country. As such, the stations in these regions with the best quality data (e.g., Bam, Esfahan, Kerman, Yazd, etc.) were selected for this research. For each year, the number of days when T d max ≥ 30 °C or T d min ≤ 0 °C were counted. Descriptive statistics and boxplots of the datasets were developed (Tables 2 and 3, Fig. 2). It must be noted that since the studied data in this research were counted event time series, the length of data is more critical, because estimating the missing values in a time series will increase the uncertainty in the results of the analysis. The selected stations do not have any gaps in data for the number of days when T d max ≥ 30 °C or T d min ≤ 0 °C.

Table 1 Identification of 30 synoptic stations which were used in this study
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Fig. 1
figure 1

Location of the synoptic stations used in this study

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Table 2 Descriptive statistics for number of days with T d max ≥ 30 °C in the selected stations during the period of 1961 to 2010
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Table 3 Descriptive statistics for number of days with T d min ≤ 0 °C in the selected stations during the period of 1961 to 2010
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Fig. 2
figure 2

Boxplots for number of days when T d max ≥ 30 °C (a) and the number of days whenT d min ≤ 0 °C (b) in the studied synoptic stations

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2.1 Test of homogeneity

When variations in a climatic variable are caused only by natural fluctuations in weather conditions, that variable has homogeneity. In other cases, especially when the location of a station is changed, the climatic variables in that station will be changed accordingly. Analysis of homogeneity in any studied data is a very important step in climatological research, especially when trend analysis is the main purpose of the study. In this research, Levene’s test was employed to examine the homogeneity in the studied data. This test is an alternative to the Bartlett test (Storch and Zwiers 1999; Brown and Forsythe 1974); the Levene test is less sensitive to the normal distribution of samples. The Levene test is defined as follows:

$$ \begin{array}{l}{H}_0:\;{\sigma}_1^2={\sigma}_2^2=\cdots ={\sigma}_k^2\hfill \\ {}{H}_a:\;{\sigma}_i^2\ne {\sigma}_j^2\hfill \\ {}W=\frac{\left(N-k\right)}{\left(k-1\right)}\frac{{\displaystyle {\sum}_{i=1}^k}{N}_i{\left(\overline{Z_{i.}}-{\overline{Z}}_{..}\right)}^2}{{\displaystyle {\sum}_{i=1}^k}{\displaystyle {\sum}_{j=1}^{N_i}}{\left({Z}_{ij}-{\overline{Z}}_{i.}\right)}^2}\hfill \end{array} $$
(1)
$$ {Z}_{ij}=\left|{Y}_{ij}-{\overline{Y}}_{i.}\right| $$
(2)

where \( {\overline{Z}}_{i.} \) and \( {\overline{Z}}_{..} \) are the groups and overall means, respectively, N is the size of total dataset and N i is the size of ith subgroup, and k is the number of subgroups. The Levene test rejects the H 0 when W > F ∝,k − 1,N − k where F ∝,k − 1,N − k is the upper critical value of F distribution with k − 1 and N − k degree of freedom and significance level of α. Homogeneity will not be present in data when H 0 is rejected in the Levene test.

2.2 Mann–Kendall (MK) trend test

The Mann–Kendall (MK) test is a non-parametric trend test which is very popular in climatology and hydrology studies (Yue et al. 2002; Gadgil and Dhorde 2005; Partal and Kahya 2006; Partal and Küçük 2006; Modarres and de Paulo Rodrigues da Silva 2007; Adamowski et al. 2009, 2010; del Río et al. 2011; Dinpashoh et al. 2011; Tabari and Hosseinzadeh Talaee 2011; Tabari et al. 2011a; Nalley et al. 2012, 2013; Shadmani et al. 2012; Wang et al. 2012a, b; Yang et al. 2012; Duhan and Pandey 2013; Safeeq et al. 2013; Shi et al. 2013; Nsubuga et al. 2014; Pingale et al. 2014; Araghi et al. 2015). By applying this test on a time series, one can detect the existence and significance of any trend in the data. The original version of the MK test entails calculating S, the number of positive differences minus the number of negative differences (Wilks 2011):

$$ S={\displaystyle \sum_{i=1}^{n-1}}\mathrm{sign}\left({x}_{i+1}-{x}_i\right)={\displaystyle \sum_{i=1}^{n-1}}\mathrm{sign}\left(\varDelta x\right) $$
(3)
$$ \mathrm{Sign}\left(\varDelta x\right)=\left\{\begin{array}{ll}+1,\hfill & \varDelta x>0\hfill \\ {}0,\hfill & \varDelta x=0\hfill \\ {}-1,\hfill & \varDelta x<0\hfill \end{array}\right. $$
(4)

where, x i is the ith ranked data in the time series and n is the length of the data records. The variance of this distribution, var(S), depends on whether all data in the time series are distinct, or whether some are repeated values. If there are no ties, the variance of the sampling distribution of S is calculated as:

$$ \mathrm{v}\mathrm{a}\mathrm{r}(S)=\frac{1}{18}\cdot \left[n\left(n-1\right)\left(2n+5\right)\right] $$
(5)

whereas, if there are ties the variance is calculated as:

$$ \mathrm{v}\mathrm{a}\mathrm{r}(S)=\frac{1}{18}\cdot \left[\left[n\left(n-1\right)\left(2n=5\right)\right]-{\displaystyle \sum_{j=1}^J}{t}_j\left({t}_j-1\right)\left(2{t}_j+5\right)\right] $$
(6)

The MK statistic, Z, is then given by:

$$ Z=\left\{\begin{array}{ll}\frac{S-1}{\sqrt{\mathrm{var}(S)}},\hfill & S>0\hfill \\ {}\ 0,\hfill & S=0\hfill \\ {}\frac{S+1}{\sqrt{\mathrm{var}(S)}},\hfill & S<0\hfill \end{array}\right. $$
(7)

where, J indicates the number of groups of repeated values, and t j is the number of repeated values in the jth group (Wilks 2011). Previous studies have shown that the existence of a seasonality pattern or serial correlation in any time series can affect the results of the MK test (Hirsch and Slack 1984; Hamed and Ramachandra Rao 1998; Yue et al. 2002). It has therefore been recommended that before applying the MK test on a dataset, one calculates autocorrelations to detect the seasonality pattern and any serial correlation in time series. The lag-k autocorrelation coefficient, r k , can be calculated as (Wilks 2011):

$$ {r}_k=\frac{{\displaystyle {\sum}_{i=1}^{n-k}}\left[\left({x}_i-{\overline{x}}_{-}\right)\left({x}_{i+k}-{\overline{x}}_{+}\right)\right]}{{\left[{\displaystyle {\sum}_{i=1}^{n-k}}{\left({x}_i-{\overline{x}}_{-}\right)}^2\right]}^{1/2}{\left[{\displaystyle {\sum}_{i=k+1}^n}{\left({x}_i-{\overline{x}}_{+}\right)}^2\right]}^{1/2}} $$
(8)

where the subscripts “−” and “+” indicate sample means over the first and last n-k data values, respectively. Equation (6) is valid for 0 ≤ k ≤ n − 1, a condition applicable to most time series. The collection of autocorrelations computed for various lags are called the autocorrelation function. Often autocorrelation functions are displayed graphically, with the autocorrelations plotted as a function of lag (Wilks 2011). To judge if observed sample data are serially correlated, the significance of the lag-1 serial correlation at a significance level of α = 0.10 of the two-tailed test is assessed using the following approximation:

$$ \frac{-1-1.645\sqrt{n-2}}{n-1}\le {r}_k\le \frac{-1+1.645\sqrt{n-2}}{n-1} $$
(9)

Hamed and Ramachandra Rao (1998) showed that when positive (negative) autocorrelation exists in times series, the estimation of variance will be less (more) than the actual value and this will in turn erroneously increase (decrease) the MK Z-value. The modified version of the MK test which must be used in such cases is as follows (Hamed and Ramachandra Rao 1998; Yue et al. 2002):

$$ \mathrm{v}\mathrm{a}\mathrm{r}\left({S}^{\prime}\right)=\frac{1}{18}\cdot \left[n\left(n-1\right)\left(2n+5\right)\right]\left[\frac{n}{n_e^{*}}\right] $$
(10)
$$ \frac{n}{n_e^{*}}=1+\left(\frac{2}{n^3-3{n}^2+2n}\right){\displaystyle \sum_{f=1}^{n-1}}\left(n-f\right)\left(n-f-1\right)\left(n-f-2\right){\rho}_e(f) $$
(11)
$$ \rho (f)=2 \sin \left[\frac{\pi }{6}{\rho}_e(f)\right] $$
(12)

where n* is the effective sample size required to account for the autocorrelation factor in the data. ρ e (f) is the autocorrelation function between the ranks of the observations and is calculated as the inverse of Eq. 10.

2.3 Sequential MK test

The sequential MK test has been recommended by the World Meteorological Organization (WMO) as an appropriate method for analyzing progressive trends and especially for detecting the onset year(s) of a trend in meteorological times series (Sneyers 1990; Partal and Kahya 2006). This test considers the relative values of all terms in a time series (x 1 , x 2 , …, x n ) and the following steps have to be performed:

  1. 1.

    The magnitudes of x j annual mean time series, (j = 1, …, n) are compared with those of x k (k = 1, …, j − 1). At each comparison, the number of cases where x j  > x k is counted and recorded in n j .

  2. 2.

    The statistic t j , as well as its mean, E(t j ), and variance, var(t j ), are calculated as:

    $$ {t}_j={\displaystyle \sum_{j=1}^{j=n}}{n}_j $$
    (13)
    $$ E\left({t}_j\right)=\frac{n\left(n-1\right)}{4} $$
    (14)
    $$ \mathrm{v}\mathrm{a}\mathrm{r}\left({t}_j\right)=\frac{j\left(j-1\right)\left(2j+5\right)}{72} $$
    (15)
  3. 3.

    The sequential values of the statistic u(t) are then calculated as:

    $$ u(t)=\frac{t_j-E\left({t}_j\right)}{\sqrt{\mathrm{var}\left({t}_j\right)}} $$
    (16)

    where, u(t) is a standardized variable with a mean of zero and standard deviation of one, which fluctuates around zero as the time series progresses. When u(t) is plotted against time, significant variations in trend are found when the u(t) curve crosses the upper or lower 95 % confidence limits (e.g., +1.96 and −1.96 for an α = 5 % significance level). In such a case, the trend can be said to have changed significantly at that point. Likewise, the u′(t) values are computed backward, starting from the end of the series. When u(t) and u′(t) lines cross each other and then continue at different slopes, the point represents the onset of a trend in the time series.

3 Results and discussions

As mentioned in Section 2.1, for Leven’s homogeneity test, the time series in each of the datasets and for any of the stations was divided into five subgroups consisting of 1961–1970, 1971–1980, 1981–1990, 1991–2000, and 2001–2010. The critical value of F 0.05, 4, 45 was approximately equal to 2.6. Results of Levene’s test for the series of T d max ≥ 30 °C and T d min ≤ 0 °C are presented in Table 4. The results show that data in all of the stations have homogeneity since the Levene’s statistic is not greater than the critical value and the p-value is not less than α = 0.05. It must be noted that counting time series which are published by the Iranian Meteorological Organization have generally been tested for homogeneity and the data have been homogenized if necessary.

Table 4 Levene’s test statistics for (a) number of days with T d max ≥ 30 °C and (b) number of days with T d min ≤ 0 °C
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In most stations the series for the number of days per annum when T d min ≤ 0 °C series showed a greater range of variation than the T d max ≥ 30 °C series (Table 2, Fig. 2). As expected, given humidity’s major role in moderating air temperature (Shelton 2009; Barry and Chorley 2009), the humid stations (Babolsar, Rasht and Ramsar) had somewhat lower values in both T d min ≤ 0 °C and T d max ≥ 30 °C series than other stations studied. Stations located in the warmer humid regions (Abadan, Ahwaz, Bandar Abbas and Bushehr) showed small to zero T d min ≤ 0 °C series values that proved generally lower than those at other stations.

Correlograms generated to detect seasonality patterns and serial correlation in each station’s time series, showed that while these series did not exhibit a seasonality pattern, there were correlations in some stations’ data. Figure 3 shows correlograms for the Sabzevar and Tehran synoptic stations. Table 5 shows the lag-1 autocorrelation coefficients (ACFs) and either standard MK Z-values (Eq. 5, ACF not significant), or MK Z values adjusted to account for significant ACF values (Eqs. 8–10) for all the time series investigated. The MK test showed trends in series of number of days when T d min ≤ 0 °C to be significant for most stations, whereas the series for T d max ≥ 30 °C were significant for fewer stations. The fact that most stations showed a negative trend in T d min ≤ 0 °C time series (Table 5), suggests that the occurrence of extreme minimum temperatures in the country will decline. This roughly concurs with previous temperature trend studies in Iran, which have shown minimum temperatures to generally increase at a higher rate than maximum temperatures (Tabari and Talaee 2011; Kousari et al. 2013). Roughly two thirds of stations have experienced a significant negative trend in T d min ≤ 0 °C series, indicating that extreme winters will be less common in the future. On the other hand, the trend for the T d max ≥ 30 °C time series is positive and significant for only 40 % of all stations. For these stations, the trend indicates that extreme high temperature events will occur with greater frequency in coming years. Returning drought conditions in most portions of the country in recent years, especially from the end of spring through the middle of autumn, concur with the present trend analysis. Given their preexisting water resource deficits, regions currently categorized as arid will suffer more from the occurrence of extreme high temperature. Clearly, this issue is a current problem in some regions in Iran (e.g., Kerman, Mashhad, Sabzevar, Shiraz, Yazd, etc.). While one might expect humid regions (e.g., Babolsar, Ramsar and Rasht stations) to have lesser variation in their temperature over time than other regions, significant positive trends were noted in humid station T d min series, and a significant positive trend was found in the T d max ≥ 30 °C series of the Babolsar humid region station. For the Bandar Abbas and Bushehr stations, T d min remained at or above 0 °C, so no ACFs or MK Z-values could be calculated for their T d min ≤ 0 °C series. Another noticeable point in this table is that the stations Shahrekord and Torbat Heydarieh were the only stations to show significant negative trends in their T d max ≥ 30 °C series, with the Torbat Heydarieh station also showing a significant negative trend in its T d min ≤ 0 °C series. This concurs with the results of previous studies regarding temperatures at the Torbat Heydarieh station (Kousari et al. 2013; Tabari and Hosseinzadeh Talaee 2011). It suggests that extreme temperature conditions will lessen at this station, which is confirmed by observations from this station in recent years.

Fig. 3
figure 3

Correlograms for Sabzevar and Tehran synoptic stations for number of days when T d max ≥ 30 °C (a) and the number of days when T d min ≤ 0 °C (b). Dotted lines indicate the confidence limits at α = 5%

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Table 5 Lag-1 autocorrelation coefficients and MK Z values for (a) number of days with T d max ≥ 30 °C and (b) number of days with T d min ≤ 0 °C (significant ACFs and MK Z value at α = 5 % are bolded)
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In the analysis of general trends in a climatological time series, and particularly in the case of climate change studies, it is important to establish the onset of any temporal trend in time series. To find these points, the sequential MK test was performed for both the number of days when T d max ≥ 30 °C and the number of days when T d min ≤ 0 °C time series, for all selected synoptic stations. Sequential MK plots for the Bam and Sanandaj stations, illustrative of different trend onsets are presented in Fig. 4. Based on the sequential MK test the onsets of T d max ≥ 30 °C trends for the different stations occurred between 1967 and 1975, whereas for T d min ≤ 0 °C series the onset occurred earlier, between 1962 and 1974 (Table 5). This indicates that the increment in T d min occurred earlier than that in T d max and that evidence of climate change was more obvious at lower temperatures. The changing of precipitation type from snow to rain is one of the major consequences of the minimum temperature trends which have occurred in Iran, even in the regions with colder climate (e.g., Tabriz, Sanandaj, etc.). This issue has been discussed in a number of recent studies (Zarenistanak et al. 2014; Farajzadeh and Karimi 2014). While changes in precipitation type are not only influenced by variations in T d min, but also by many other factors (Raziei et al. 2012, 2013; Ghasemi and Khalili 2006), the important role of changes in T d min in altering precipitation type is a foundational concept in meteorology (Ahrens 2009; Lutgens and Tarbuck 2013) as has been confirmed by previous studies in Iran (Rahimzadeh et al. 2009). Because of the natural complexity in precipitation formation, changes in precipitation are expected to begin later than changes in temperature. This is confirmed by previous studies showing the onset of changes in precipitation in different locations in Iran to have occurred between 1979 and 1992 (Shifteh Some’e et al. 2012), compared to 1975, the latest onset of changes in temperature determined in the present study. As can be seen in this figure, approximately most parts (67 % of stations) of Iran have experienced a significant negative trend in the number of days where T d min ≤ 0 °C, while a significant positive trend in the number of days where T d max ≥ 30 °C was only apparent in 40 % of all stations (Fig. 5). This indicates that at present climate change has had greater effects on the minimum temperature in Iran and is expected to influence maximum extreme temperatures to a greater extent in coming years.

Fig. 4
figure 4

U(t) and U’(t) plots for (a) station of Bam (for the number of days when T d max ≥ 30 °C) and (b) station of Sanandaj (for the number of days when T d min ≤ 0 °C). (Note: U(t) and U’(t) are sequentially illustrated by solid and dotted line)

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Fig. 5
figure 5

Significant trends for series (a) the number of days when T d max ≥ 30 °C and series (b) the number of days when T d min ≤ 0 °C. (Note: black (gray) triangles indicate positive (negative) trend and circles show non-significant trends)

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4 Conclusions

The number of days when extreme temperature conditions occurred in 30 synoptic stations in Iran during the period of 1961 to 2010 was examined. First, the MK test was used to determine trends in the time series and the sequential MK was then employed to detect the onset of the existing trends. The fact that the number of days when T d min ≤ 0 °C showed a significant negative trend in 67 % of all stations studied, while the number of days when T d max ≥ 30 °C showed a significant positive trend in only 40 % of the stations, indicates that the T d min ≤ 0°C decreased at a greater rate than the increase T d max ≥ 30°C within the country. This suggests that a hydrological crisis (e.g., droughts, dry spells, etc.) is likely to develop in coming years, particularly since the precipitation type is likely to be affected. A change in precipitation type and repetitive droughts are two major consequences which have already been observed in Iran, especially in the last two decades. Results of the sequential MK test show that the trend in the number of days when T d max ≥ 30 °C time series began between 1967 and 1975, whereas the equivalent trend for T d min ≤ 0 °C began earlier, between 1962 and 1974. This suggests that in the future, problems created by extreme maximum temperatures will increase. The important effects of temperature patterns (especially minimum temperature) on water demands will be one of the critical subjects of future studies in this field, because when precipitation type is permanently altered, stored water will be lost faster and water demands will rise accordingly. Such studies are important to facilitate the transition to more integrated and adaptive forms of water resources management (Halbe et al. 2013, 2014) in the arid and semi-arid regions of the world, where limited water resources are a critical issue.