1 Introduction

Temperature, among the various dominant atmospheric variables, has a significant and direct influence on almost all hydrological variables (Sonali and Nagesh Kumar 2013). Several studies have reported that temperature is increasing owing to rise in greenhouse gases and human activities (Feidas et al. 2004). According to the Intergovernmental Panel on Climate Change (IPCC 2007), the mean air temperature of global surface has increased by 0.74 ± 0.18 °C during 1906–2005, which is likely related to the increased human activities and anthropogenic greenhouse gas concentrations (You et al. 2013). The analysis of long-term trends constituting such changes in climatic variables as temperature is a crucial target in studies on climate variability and change detection (Ghasemi and Khalili 2008). Several researchers have studied the long-term trend of temperature series across the world (Salinger 1995; Przybylak 2001; Yue and Hashino 2003; Machiwal and Madan 2006; Staudt et al. 2007; Esteban-Parra et al. 2007; Zhang et al. 2009; Mamtimin et al. 2011; Martinez et al. 2012; Dasha et al. 2012; Boccolari and Malmusi 2013; Gocic and Trajkovic 2013). Kousari et al. (2011) studied trend of mean, minimum and maximum air temperature, precipitation and relative humidity based on the Kendal test in Iran and suggested an increasing trend for air temperature while a decreasing one for precipitation and relative humidity at the majority of the studied stations. del Rio et al. (2013) employed statistical tests in Pakistan in order to determine the recent mean temperature trend and revealed that the temperature has generally increased in Pakistan at all-time analyzed scales over the past decades.

Urmia Lake basin, one of the six large basins in Iran, has been shrinking for the recent 15 years. As a consequence, the water surface area has decreased from 6100 to 4750 km2, while its water level declining about 6 m (Fathian et al. 2014). Shokoohi and Morovati (2015) in their research showed that the Urmia Lake basin faced the most severe drought condition but it cannot be only reason for the lake dry up; however, some human activities such as dam construction, overexploiting of surface and groundwater during drought periods could be effective in intensifying the natural drought effects. The changes in hydrological parameters such as precipitation and evaporation may occur due to the perceptible increases in the surface temperature. The existence of an uptrend or downtrend in a hydrological time series can also be described by changes in surface air temperature as one of the most effective meteorological driver in the hydrological processes. Therefore, a trend analysis of air temperature is the first step to investigate the probable causes of declaring water level in Urmia Lake basin.

Several researches have been carried out to examine the surface air temperature trends in Iran over the last decades; however, no comprehensive basin scale based efforts have been to determine air temperature. In other words, most of the researches were focused on provincial boundary instead of the watershed boundary. Moreover, most of the former investigations did not consider the serial correlation of the air temperature time scales and their probable adverse impacts on such trend tests as MK test. The primary aim of present research is to assess the effect of serial correlation on Tmean, Tmax and Tmin series based on the MK test. The secondary objective is to analyze spatio-temporal trends in Tmean, Tmax and Tmin air temperature at the monthly, seasonally and annually scales by utilization of interpolation technique including Modified MK, Mann–Whitney (MW), linear regression and Sen,s slope estimator tests. Finally, the shift and abrupt changes were considered based on the MK rank statistic and change point tests including; Buishand’s, SNHT, Pettitt’s tests. Thus, analysis of the variations in temperature will help us to better understand of the climate variability in the Urmia Lake basin (ULB).

2 Material and Methods

2.1 Study Area and Data

Located in northwest of Iran, Urmia Lake basin covers a catchment area of 51, 800 km2. It is one of the six main river basins of Iran which consists of 14 main sub-basins. Urmia Lake basin has three most important rivers, namely, Aji Chai, Zarrineh Roud and Simineh Roud. Located in center of the basin, Urmia Lake is the second largest hyper saline lake in the world that experience serious decreasing in water level and surface area which has led to its alarmingly shrinking status. In this work, Tmean, Tmax and Tmin temperature series collected from the 15 gauging stations within the basin which had the valid and adequate data for the period of 1972–2011. The geographic location of temperature gauge stations are shown in Fig. 1.

Fig. 1
figure 1

Spatial distribution of the stations in the ULB

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2.2 Methods

2.2.1 Mann-Kendall Test

The Mann–Kendall test is a non-parametric test, with no requirement to the normal distribution of data. The null hypothesis H o indicates that the depersonalized dataset (x 1,…, x n ) is a sample of n identically distributed and independent random variables while the alternative hypothesis of a two-sided test (H 1 ) means that the distribution of x k and x j are not identical for all k, j ≤ n with k ≠ j. The test statistic S is a asymptotically normal which has mean zero and a variance computed by Eqs. (1) and (2) (Partal and Kahya 2006):

$$ S={\displaystyle \sum_{k=1}^{n-1}}{\displaystyle \sum_{j=k+1}^n}sgn\left({x}_j-{x}_k\right) $$
(1)
$$ sgn\left({x}_j-{x}_k\right)=\left\{\begin{array}{c}\hfill +1\kern1.25em if\kern0.5em \left({x}_j-{x}_k\right)>0\hfill \\ {}\hfill 0\kern1.5em if\kern0.5em \left({x}_j-{x}_k\right)=0\hfill \\ {}\hfill -1\kern1em if\kern0.5em \left({x}_j-{x}_k\right)<0\hfill \end{array}\right. $$
(2)
$$ Var(s)=\frac{n\left(n-1\right)\left(2n+5\right)-{\displaystyle {\sum}_t}t\left(t-1\right)\left(2t+5\right)}{18} $$
(3)

where t is the extent of any given tie while ∑t states the summation over all ties. When the sample size n >10, the standard normal variable Z is calculated using Eq. (4) (Tabari and Marofi 2011):

$$ z=\left\{\begin{array}{c}\hfill x=\frac{s-1}{var(s)}\hfill \\ {}\hfill 0\hfill \\ {}\hfill x=\frac{s+1}{\sqrt{var(s)}}\hfill \end{array}\right.\ \left\{\begin{array}{c}\hfill if\ s>0\hfill \\ {}\hfill if\ s=0\kern0.5em \hfill \\ {}\hfill if\ s<0\hfill \end{array}\right. $$
(4)

In a two-sided trend test, the H 0 should be accepted if |Z| ≤ Z α/2 at the α level of significant. Therefore, a positive value of S indicate an “upward trend” and a negative value indicate a “downward trend” (Partal and Kahya 2006). The significance levels of α = 0.01 and 0.05 were considered in this research.

2.2.2 Sen’s Slope Estimator

Sen (1968) introduced a simple non-parametric procedure to estimate the true slope of a linear trend in a time series. The slope which estimates N pairs of data are calculated by:

$$ {Q}_i=\left(\frac{X_i-{X}_k}{i-k}\right)\mathrm{f}\mathrm{o}\mathrm{r}\ i=1, \dots,\ N $$
(5)

where x j and x k are data value at time i and k (i > k), respectively. The Sen,s estimator of slope is defined as the median of N values of Q i . If N is even, then Sen,s estimator is computed by Q med  = [Q N/2 + Q (N + 2)/2]/2N while if it is odd, the estimator is computed by Q med  = Q (N+1)/2 . Finally, the true slope can be computed by a non-parametric test and Q med is checked by a two-sided test at the 100 (1-α)% confidence interval (Partal and Kahya 2006; Tabari and Hosseinzadeh Talaee 2011).

2.2.3 Mann–Whitney Test

The Mann–Whitney test is a nonparametric approach and an alternative for the t- test for two independent samples. It can be used to test whether two independent samples have been taken from the same population (McCuen 2002). The MW test statistic U is given by Yue and Wang (2002) as follows:

$$ U= min\left\{{U}_1,\ {U}_2\right\} $$
(6a)
$$ {U}_1={n}_1{n}_2+\frac{n_1\left({n}_1+1\right)}{2}-{R}_1 $$
(6b)
$$ {U}_2={n}_1{n}_2+\frac{n_2\left({n}_2+1\right)}{2}-{R}_2 $$
(6c)

where U 1 is the total number of sample I observations preceding sample II observations, and U 2 is the total count of sample II observations preceding sample I; n 1 and n 2 are the size of sample I (X 1 ) and sample II (X 2 ), respectively; and R 1 and R 2 are the rank sums of the samples X 1 and X 2 , respectively. When the null hypothesis, H 0 , is true and when n 1 and n 2 are both larger than 8, U is approximately normally distributed with mean of E(U) and variance of V(U) as (Yue and Wang 2002):

$$ E(U)=\frac{n_1{n}_2}{2} $$
(7)
$$ V(U)=\frac{n_1{n}_2\left({n}_1+{n}_2+1\right)}{12} $$
(8)

2.2.4 Linear Regression

In this research, the magnitude of the trends was considered to be statistically significant based on the Student’s t-test at α = 0.05 level.

2.2.5 The Effect of Serial Correlation on MK Test

According to the null hypothesis of the MK test, the dataset is independent and randomly ordered which means no serial correlation and trend among the observations (Hamed and Rao 1998). The existence of positive serial correlation will increase the possibility of rejecting the null hypothesis of no trend, while the null hypothesis is true. The temperature time series might show serial correlation more than other climatic variables (Yue and Hashino 2003). Hence, it is necessary to consider the effect of serial correlation on the MK test. The possible significant trends in air temperature observations are examined by using the following procedures:

  1. I.

    Compute the lag-1 serial correlation coefficient (designated by r 1 ).

  2. II.

    If the calculated r 1 is not significant at the 5 % level, then the Mann–Kendall test will be applied to original values of the time series.

  3. III.

    If the calculated r 1 is significant, prior to application of the Mann–Kendall test, then the ‘pre-whitened’ time series may be obtained as (x 2 -r 1 x 1 , x 3 -r 1 x 2 , …, x n -r 1 x n-1 ) (Partal and Kahya 2006; Tabari et al. 2011).

In this study, existence of serial correlation within air temperature dataset was examined by using Ljung-Box Q k at α = 0.05 significance level. At k lag, the Q k statistic is calculated by using following formula (Ljun and Box 1978):

$$ {Q}_k=n\left(n+2\right){\displaystyle \sum_{l-1}^k}\frac{r_l^2}{n-l} $$
(9)

If n is large, Q k has a chi-square distributions with degree of k-p-q, where p and q are autoregressive and moving average orders, respectively. The significance level of Q k is calculated by chi-square distribution with k-p-q degree of freedom.

2.2.6 Change Point Analysis

There are many methods for analyzing change points or starting an increasing or a decreasing trend in temperature time series (Tabari et al. 2012). In this paper, four important methods for detecting change points including; Mann–Kendall rank (Sneyers 1990), Pettitt’s test (Pettitt 1979), SNHT (Alexandersson 1986) and Buishand’s (Buishand 1982) were used.

3 Results and Discussion

3.1 Lag-1 Serial Correlation

Generally, positive serial correlation was identified for 38, 53 and 31 % of whole time series for the Tmean, Tmax and Tmin, respectively. Annual series had the greatest number of significant positive correlation and summary of the lag-1 serial coefficient for area-averaged series are presented in Fig. 2. Area-averaged monthly series showed that March with coefficient values of 0.34 and 0.36 had the highest Ljung-Box coefficient, while April with values of 0.003 and 0.014 resulted the lowest coefficient for the Tmean and Tmax, respectively. Furthermore, similar to the Tmean and Tmax, Tmin had the lowest Ljung-Box coefficient with the value of 0.13 in the April, while the highest value (i.e. 0.39) was found in the August.

Fig. 2
figure 2

Lag-1 serial correlation coefficient of area-averaged monthly and seasonal temperature series

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3.2 Trends in Tmean, Tmax and Tmin

The significant serial correlation was eliminated for analyzing the influence of serial correlation on the MK test (Fig. 3). The results of original and pre-whitening monthly series determined the different influences of serial correlation on the MK test. Generally, the positive serial correlation on the Tmin had the most influence on increasing the possibility of rejecting the null hypothesis of no trend, while the null hypothesis is true. Therefore, in this study the influence of positive serial correlation on the MK test showed necessity of pre-whitening temperature series prior to implementation of MK test in the trend analysis as emphasized by some other researches (Yue et al. 2002; Kumar et al. 2009; Shadmani et al. 2012).

Fig. 3
figure 3

Significant trends in original and pre-whitened series (a is monthly series and b is seasonal and annual series)

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The results of the MK test show positive trends in the Tmean, Tmax and Tmin in most of months (Table 1). In the monthly Tmean series, the MK test in all of the stations identified significant positive trends at the 0.05 significance level except April, July, November and December. In the Tmean series, the large number of stations (i.e. 93.33 %) had significant warming trends at the 0.05 significance level in May. Also, in the Tmax series 93.33 % of the stations had a warming significance trend in March and June. Similar to Tmax, analysis of Tmin indicated the strongest significant warming trend in March for 80 % of the stations. However, the monthly Tmean, Tmax and Tmin series showed the highest significant warming trends in May, March to June and March, respectively.

Table 1 The results of the MK test for the monthly temperature time series
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Three stations, Sad Noroozlou, Pol Sorkh and Sad Shahid-Kazemi which located in the south of the basin mostly showed the significant cooling trends in the Tmean and Tmax. This means that trend of temperature series in the ULB were positive and negative. Soltani and Soltani (2008) reported similar results in the northern Iran for the Tmin and Tmax series.

The inverse distance weighted interpolation technique was used for the seasonal and annual series in order to explore the spatial trends over ULB. Spatial distribution results of modified MK test for the seasonal and annual scales in the study region are shown in Fig. 4. In the winter series, 66, 86 and 53 % of the stations, which are located at the vicinity of the Lake, were found with increasing trend of Tmean, Tmax and Tmin at the 0.05 significance level. The increasing trends of Tmean, Tmax and Tmin series in this research have a good fit with the results in other regions such as China (Mamtimin et al. 2011), Turkey (Turkes and Sumer 2004) and Jordan (Smadi 2006).

Fig. 4
figure 4

Spatial distribution of the MK test for the seasonal and annual series (a, b and c indicate the Tmean, Tmax and Tmin, respectively, and bold values indicate the significant trends at the 0.05 level)

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The MW test was used to determine the shift changes after dividing the annual temperature series into two groups pre -1991 and post 1991 (Table 2). In general, 86, 73 and 80 % of the stations have experienced significance upward shift change at the 0.05 level over the four decades in the annual Tmean, Tmax and Tmin series, respectively. Furthermore, the results of MW test for shift change detection showed good fit with the outputs of MK test.

Table 2 The results of MW test for the annual temperature series in the ULB
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3.3 Magnitude of Trends

The Sen,s slope estimator for temporal along with linear regression for spatial trend was used to identify the magnitude of increasing or decreasing trends in ULB. The results of the Q med of Sen,s estimator for the monthly air temperature series are given in Fig. 5. As shown, the Ghasemloo, Marz Sero, Sahlan, Tazekand and Yalghouz Aghaj stations which are located in the vicinity of Urmia Lake presented a warming trend in all of the series over 12 months. Among the above mentioned stations, the Marz Sero station located in the west of the Lake showed the most warming trends over the four decades in whole air temperature series Fig. 6.

Fig. 5
figure 5figure 5

The Qmed of Sen’s estimator for the monthly Tmean, Tmax, and Tmin series in ULB

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Fig. 6
figure 6

The linear regression slope (b) for the annual Tmean, Tmax and Tmin series in the ULB

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Generally, area-averaged temperature series in the monthly scale indicated variation of Tmean from (+) 0.39 to (+) 1.22 °C per decade. Meanwhile, February and March with value of (+) 1.09 and (+) 1.22 °C had the highest magnitude of warming trends. In addition, results also showed the highest values in February and March with the value of (+) 1.11 and (+) 1.45 °C per decade in Tmax and value (+) 1.11 and (+) 1.22 °C in Tmin. Hence, among the air temperature series, magnitude of a warming trend in Tmax in the mentioned months is more than Tmean and Tmin. On other hand, magnitude analysis of the air temperature monthly series revealed considerable increase in March and February. We also identified the highest magnitude of warming trend in most of the stations in the monthly Tmax series especially in February and March. This is a good point to understand the impacts of warming trends in temperature series of the Urmia Lake. At this semi-arid region, most of rainfall and snow falling occurs in the winter and extended time of shortage precipitation leads to scarcity of water yield in the rivers which drain to the Urmia Lake. Shifteh Some’e et al. (2012) suggested a noticeable decreasing trend in winter precipitation series of the northern Iran. Meanwhile, increases in air temperature in February and March could increase the evaporation and evapotranspiration trends (Sabziparvar et al. 2010; Dinpashoh et al. 2011), which may lead to changes in water temperature. Moreover, the mountainous basins such as ULB, are relatively vulnerable environments to the climate change, due to of their watershed properties which are very sensitive to temperature changes (Birsan et al. 2005; Abghari et al. 2013).

The spatial distribution of significant trends based on the slope of linear regression (b) for the annual air temperature series revealed increasing trends with the values ranging from 0 to 0.75 °C in the Tmean, Tmax and Tmin series at the 0.05 % significance level over the studied period. Therefore, results showed that the basin suffered from increasing trends of Tmean, Tmax and Tmin over the past decades. Consequently, interpolation maps suggested higher warming trends in the western and eastern parts of the basin than southern part.

3.4 Change Points Analysis

Detecting the change points (or mutation point) in the surface air temperature series was considered to understand the correlation between the climate variability and decreasing water level of Urmia Lake. For determination of the approximate beginning year of the significant trends, the Mann-Kendall rank and change point tests were used. The results of this test for the annual air temperature series in the stations obviously showed the beginning of trend at the 0.05 significance level. In the Yalghouz Aghaj and Mir Abad stations the Mann-Kendall rank test showed the approximate years of beginning of the significant trends were in 1992 and 1983 for the Tmean series. In the Tmax series, the Shanjan and Marz Sero stations showed that the beginning years were 1986 and 1984, and also for the Tmin in the Oshnavieh and Tazekand stations the years were 1992 and 1982, respectively. However, the Mann-Kendall rank test for the air temperature series determined that beginning of significant trends in some stations showed at 1980s and others ones were in 1990s.

Three commonly used change points tests namely, Pettitt’s test, SNHTz and Buishand’s were chosen for the monthly, seasonal and annual temperature series (Table 3). The results showed that only April is homogenous in the monthly, seasonal and annual series. In contrary, most of the air temperature series are heterogonous around year of 1992 according to the three tests. On the other hand, in the Tmean series about 50, 70 and 57 % of significant change points are around 1992 by Pettitt’s, SNHT and Buishand’s tests, respectively. Furthermore, in 1992, we found 46, 57 and 66 % significant uptrend changes in Tmax series while 66, 54 and 60 % in the Tmin series by Pettitt’s, SNHT and Buishand’s tests, respectively. However, more than 90 % of total significant change years in air temperature series were found in 1990s. Averagely, three tests confirmed the positive significant mutation points in the Tmean, Tmax and Tmin in 73, 71 and 60 % of the stations started in 1990s, respectively. The results of the change points showed a good fit to the results observed in southwestern Iran (Zarenistanak et al. 2014).

Table 3 The most probable change year of the monthly, seasonal and annual temperature series
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The results of Mann-Kendall rank and change year tests explained that, year of changing point up to increasing in most of the stations and temperature series was in the 1990s whereas, based on the Mann-Kendall rank test, some stations had such situation in 1980s. Generally, significant change year based on the mentioned methods was found in 1980s and 1990s. A drastic decrease of more than 5 m in the water level of Urmia Lake began in 1990s (Fathian et al. 2014). In this study, it is noticeable that the significant change years of warming trends are close to the beginning of water level decrease in Urmia Lake. Climate change and variability is expected to be more intensive over the next century, due to the ever increasing rate of greenhouse gases emissions (Ashrafi et al. 2012; Manju et al. 2012). Increasing temperature would have some influences on the regions including: increase of the energy demand for cooling, reduce the precipitation amount and consequently dramatic reduction of water resources of the Urmia Lake (Roshan et al. 2010; Roshan et al. 2011; Tisseuil et al. 2013).

4 Conclusions

The long-term trends in monthly, seasonal and annual mean, maximum and minimum air temperatures of the gauge stations of ULB were investigated over the period 1972–2011. The tests conducted on the monthly series detected significant warming trends in the Tmean series which were larger than those in Tmax series, and also Tmax was found more than Tmin series. Furthermore, the significant warming trend of Tmax in most of the stations in winter was more than of Tmean and Tmin. The spatial distribution of the Modified MK test for the seasonal and annual scales demonstrated that most of the observed trends in the seasonal and annual air temperature series were positive at the 0.05 significance level. Moreover, the results of MW test in this study for shift change detection are in a good fit to outputs of MK test.

On average, the results of Sen’s slope estimator showed the magnitude of significant warming trends in annual Tmean, Tmax and Tmin was (+) 0.58, (+) 0.52 and (+) 0.69 °C per decade, respectively. Overall, although Tmin increased at the higher rate than Tmean and Tmax, the results revealed similar increasing trends for the air temperature series. The interpolation maps showed that warming trends in the east and west of Urmia Lake were more than southern area. Intensive industrialization and urbanization in the west and mostly in the eastern part of the Lake could be considered as a reason of most warming trends in temperature series in the west and eastern sides.

Generally, in this research significant change year was found in 1980s and 1990s. In this study, it is interesting that significant change years of warming trends are close to the beginning of decreasing water level of the Lake. Consequently, it can be suggested that the warming trends in the temperature series had adversely impacted on the Lake over the past decades.