1 Introduction

The Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change (IPCC) shows that the globally averaged surface temperature of the Earth and oceans has increased about 0.85 °C (0.65–1.06 °C) during the period 1880 to 2012. Therefore, global warming is inevitable (IPCC, 2013). The effects of global warming are closely related to the increase in the frequency and severity of extreme events such as floods, droughts, and heat and cold waves, rather than to changes in the average climate condition (Peterson et al. 2013). Changes in extreme events of temperature (ETI) affect many aspects of human life, such as water resources (Xu et al. 2010), public health (Piticar et al. 2018), agriculture (Ju et al. 2013), energy (Añel et al. 2017), and mortality (Barnett et al. 2012). A period of consecutive days with very high and low temperatures is called a warm or cold wave (Cook et al. 2013). They are forms of extreme climate events, and their frequency, intensity, and duration are expected to increase under climate change in the next decades (Thornton et al. 2014). Increasing in frequency and intensity of temperature extremes is significant for detecting cold spells in the region with dry climates such as Iran, which depends on snowmelt water resources in the warm period of the year. Donat et al. (2013) showed that significant warming in all seasons is associated with more pronounced warming in cold seasons of the Earth.

Studies examining the minimum and maximum temperatures of Iran using the output of CMIP5 (Fallah-Ghalhari et al. 2019) and CMIP6 (Zarrin & Dadashi-Roudbari, 2020) models have reported an increase in the minimum temperature, especially for the mountainous regions of Iran that it is a serious threat to water resources.

Therefore, the projection of seasonal extreme events has great importance in studies related to water resources (Piao et al. 2010), agriculture (Bindi & Olesen, 2011), and bioclimatology (Strelcová et al. 2008). The essential tools for studying the future climate are general circulation models (GCMs). These models are also valuable to simulate the historical period. The output of general circulation models also used to project extreme events around the world, and their output evaluated (Kharin et al. 2013; Sillmann et al. 2013; Wuebbles et al. 2014; Dong et al. 2015; Alexander & Arblaster, 2017; You et al. 2018; Ongoma et al. 2018; Xu et al. 2019a, 2019b; Yu et al. 2020). However, what needs more attention regarding the use of GCMs is the high uncertainty of these models. To reduce model uncertainty, a new generation of these models called Earth system models (ESM) developed that involves interaction between different parts of the climate system (including the atmosphere, ocean, land ice, and sea) and the exchange of energy and mass (Knutti and Sedlacek, 2013). In this version of the models, chemical processes, land use, plant and ocean ecosystems, as well as the carbon cycle included which allows the integration of biochemical processes in the Earth system (Heavens et al. 2015). The ESM model series is the base of the Coupled Model Intercomparison Project (CMIP) (Carvalho et al. 2017). Despite this significant achievement in the CMIP model series, there is still a great deal of uncertainty. Although the uncertainty may not be a big deal when looking into the values of annual or seasonal averages, it becomes a serious challenge when the goal is to study extreme events.

However, three strategies proposed to reduce uncertainty: (1) downscaling (dynamical or statistical approaches) (Manzanas et al. 2018); (2) bias-correction (BC) (Navarro-Racines et al. 2020); and (3) multi-model ensemble approach (Tegegne et al. 2020). Dynamical downscaling methods are time-consuming (Xu et al. 2019a, 2019b), and because of the lack of hardware infrastructure in developing countries such as Iran, using this method is not efficient. Therefore, the multi-model ensemble (MME) (Tegegne & Melesse, 2020; Tegegne et al. 2020) and bias-correction methods (Maraun, 2016) are better choices adding more values. It is especially important when the MME based on a bias-corrected method, which significantly reducing the uncertainty. Another important point on the projection of temperature extremes (specifically hot and cold spells) is the lack of universal definition (Stephenson et al. 2008). Overviewing the literature shows that different researchers have mainly used three methods: (1) using an absolute threshold (e.g., five consecutive days with a temperature between 30–35 °C) (Suparta and Yatim, 2017); (2) the use of percentile values (Kent et al. 2014), and (3) combined indices of different meteorological variables according to the guidelines approved by the World Meteorological Organization (WMO), such as Expert Team on Climate Change Detection and Indices (ETCCDI) (Alexander et al. 2006; WMO, 2010; Hong et al. 2018). In this research, the third approach was used.

The importance of temperature extremes has led to a wide range of studies. The review of the literature reveals that these studies can methodologically be divided into different categories. It included monitoring temperature using gauge data (Merlone et al. 2019; Sheridan et al. 2020), reanalysis dataset (Zhu et al. 2017; Donat et al. 2016; Sheridan et al. 2020), and satellite products (Mushore et al. 2018; Azarderakhsh et al. 2020), and projecting future climate. The methods of future projections of temperature extremes can be divided into different categories based on a direct output of models (Alexander & Arblaster, 2017; LUO et al. 2020), statistical downscaling (Ali et al. 2019; Yang et al. 2019), dynamical downscaling (Bozkurt et al. 2019; Zhu et al. 2020), studies based on bias-correction output (Gao et al. 2019; Xu & Wang, 2019; Navarro-Racines et al. 2020), and MMEs (Tegegne et al. 2020; Tegegne & Melesse, 2020). Extreme temperature of Iran considered by many researchers in recent years. The main part of these studies is investigating them using gauge data (Rahimzadeh et al. 2009; Soltani et al. 2016; Rahimi & Hejabi, 2018; Fallah-Ghalhari et al. 2019). Future climate projections also rely on downscaled datasets for a particular station or geographic area (Vaghefi et al. 2019; Fallah-Ghalhari et al. 2019; Naderi et al. 2020).

A review of temperature extremes has shown that even though many global studies use gridded data, they have received less attention in Iran. Since Iran is a large area with a complex topography and has climate diversity, gridded data that can cover the entire area of the country compared to previous research that used only station data is an advantage of this research. Also, bias-correction and multi-model ensemble (MME) methods are used for projecting temperature extremes in Iran for the first time.

This study aimed to project the seasonality of ETIs by emphasizing TX, TN, WSDI, and CSDI from ETCCDIs indices. Two newly introduced ETI including the maximum number of consecutive frost days (CFD) and the maximum number of consecutive summer days (CSU), seasonality, and the CMIP5 BC MME approach are used for the first time in Iran.

Based on the purpose of this research, in the first step, the ensemble of selected CMIP5 bias-correction models is generated using the independence weighted mean (IWM) method. Then TX, TN, WSDI, CSDI, CFD, and CSU indices for the duration of cold and heat waves, frost, and summer days of Iran using two scenarios, RCP4.5 and RCP8.5 are studied. The achievement of this study is significant for the fields of public health, water resources, and agriculture in Iran.

2 Material and methods

2.1 Study area and dataset

Iran has an area of 1,648,195 km2, which is located in southwest Asia with an arid and semi-arid climate (Fig. 1). One-third of Iran is covered by mountains, most of its remaining parts include dry plains and deserts, and only less than a quarter of that is cultivable. The existence of mountain ranges such as Zagros and Alborz are associated with severe temperature fluctuations in Iran. In this study, we have shown that the minimum temperature in winter reaches − 8.53 °C, and the maximum reaches 44.8 °C in summer. Since most of agriculture is rainfed, and its freshwater resources are highly dependent on snowmelt, any variability in temperature, especially the increased heat waves, is associated with many issues for vulnerable water resources and agriculture of Iran.

Fig. 1
figure 1

a Spatial distribution of synoptic stations over Iran, with digital elevation model (DEM), derived from the SRTM elevation data (~ 1 km2) and, b CMIP5 grid (0.5°). These synoptic stations provided consistent observations during 1965–2005.

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2.2 Data

2.2.1 Observation dataset

The observation dataset is the homogeneous time series of daily maximum and minimum temperatures of 40 synoptic stations (Fig. 1). The gauge data were obtained from the Meteorological Organization of Iran (IRIMO) (https://www.irimo.ir). The selected stations were subjected to strict quality control, which included identifying and correcting aberrant points in the long-term climate time series and covering the gaps. To ensure data quality, in the first stage, stations that had a large number of data gaps or were missing for at least 10 years were excluded. Then, the station dataset were analyzed for extreme data points, and data with more than four times the standard deviation value were excluded from the monthly averages. Station data used only to evaluate CMIP5 data with a 40-year time series (1965–2005), as shown in Fig. 1.

2.2.2 CMIP5 bias-correction multi-models

In this research, five CMIP5 BC MME were used. Both the minimum and maximum temperature indices were obtained from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) archive for the first realization (r1i1p1f1) (see Table 1). In the ISIMIP project for bias-correction of CMIP5 climate data, EartH2Observe, WFDEI, and ERA-Interim data have merged to bias-correct the ISIMIP (EWEMBI) (Lange, 2018).

Table 1 CMIP5 models supplied by the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) archives were used in this research
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2.2.3 The WFDEI meteorological forcing dataset

The WFDEI meteorological forcing dataset has been generated using the ERA-interim reanalysis data. The WFDEI will allow more direct comparisons of hydrological and Earth system model outputs with hydrologically and phonologically relevant satellite products (Weedon et al. 2014).

2.2.4 The representative concentration pathways (RCP) scenarios

The two periods 1965–2005 and 2021–2099 were considered as historical and projection periods, respectively. Also, two scenarios, representative concentration pathway 4.5 RCP4.5 and RCP8.5 (Table 2), were selected to project extreme temperatures in Iran.

Table 2 Representative concentration pathway (RCP) scenarios used in this research
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2.3 Methodologies

2.3.1 Spell length duration indices (SDI)

In this paper, CSDI and WSDI indices were used for assessing spell length duration (Moss et al. 2010) in Iran (Table 3). The World Meteorological Organization Commission on Climatology (CCl) and the Climate Variability and Prediction (CLIVAR) Expert Team on Climate Change Detection and Indices (ETCCDIs) jointly developed a core set of indices (Anandhi et al. 2016). In these indices, spells end each season and do not continue to the next season on a seasonal scale. Thresholds of 90th and 10th percentiles of Tmax and Tmin calculated using the method described by the ETCCDIs for each day of each season (Zhang et al. 2009).

Table 3 Definitions of 2 spell duration indices (SDI)
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2.3.2 Skill of the models in representing the seasonal temperature

The Taylor diagram is applied to highlight the preciseness of different models in comparison with observations. This method shows the changes in the observed values compared to the modeled value according to the standard deviation and root mean square deviation (RMSD) (Kumar et al. 2014).

2.3.3 Independence Weighted Mean (IWM)

The analysis of individual models does not provide suitable results due to their high uncertainty. Also, these results are not proper for adaptation and adjustment policies and make the research too theoretical rather than directing it to a practical field. In this regard, we used the output of 5 selected CMIP5 bias-correction models, the details of which are given in Table 1, using a multi-model ensemble (MME) method called independence weighted mean (IWM). This method was developed by Bishop & Abramowitz (2013). For further reading, see Bishop and Abramowitz (2013) and Bai et al. (2020). This method was computed as in Eq. (1).

$${\sum}_{j=1}^J{\left({\mu}_e^j-{y}^i\right)}^2 where\ {\mu}_e^j={w}^T{x}^j={\sum}_{k=1}^K{w}_k{x}_k^i$$
(1)

In Eq. (1), (1,…, j,…, J) is the time step of daily minimum (TN) and maximum (TX) temperature values, (1,…, k,…, K) is the selected CMIP5 GCMs in this study, \({\mu }_{e}^{j}\) is ensemble minimum and maximum temperatures of multiple models, \({j}_{th}\) is the time step, \({y}^{i}\) represents the \({j}_{th}\) time step in the observation period, w is the weight of each model from the set of ensemble models, and finally, \({x}^{j}\) is the model coefficient in linear composition (Bishop and Abramowitz, 2013; Bai et al., 2020; Zarrin & Dadashi-Roudbari, 2021). Then, in the next step, Eq. (2) was used to ensure that \(\sum_{k=1}^{k}{w}_{k}=1\), the constraint term is solved by the Lagrange multiplier.

$$F\left(w,\lambda \right)=\frac{1}{2}\left\lceil \frac{1}{J-1}{\sum}_{j=1}^J{\left({\mu}_e^j-{y}^i\right)}^2\right\rceil -\lambda \left(\left({\sum}_{k=1}^k{w}_k\right)-1\right)$$
(2)

In Eq. (2), \(w\) was calculated based on Eq. (3).

$$w=\frac{{A}^{-1}1}{{1}^{T}{A}^{-1}1}$$
(3)

In Eq. 3; \({1}^{T}=\left[\mathrm{1,1},\dots ,1\right]\); A is the sample-based estimate of the covariance of the bias-corrected errors between all of the ensemble members (Bai et al., 2020; Zarrin & Dadashi-Roudbari, 2021).

Finally, the value of A was calculated by Eq. (4)

$$\mathrm{A}=\frac{\sum_{j=1}^{J}({x}^{j}-{y}^{j}){({x}^{j}-{y}^{j})}^{T}}{J-1}$$
(4)

2.3.4 Mean of daily Minimum and maximum temperature (TN & TX)

To demonstrate the long-term changes of the minimum and maximum temperatures of Iran during the historical period (1965–2005) and the projected future period (2021–2060 and 2061–2100), the mean minimum (TN) and maximum (TX) data of the CMIP5 BC MME were used (Table 4). These two indices are widely used for studies related to climate variability and change and are the primary input data for calculating ETIs.

Table 4 Definition of the minimum (TN) and maximum (TX) temperatures
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2.3.5 Maximum number of consecutive frost and summer days (CFD and CSU)

The ETCCDI climate indices have been the subject of much research in recent years, and as mentioned in the introduction, many studies of the ETIs were conducted in Iran, both for observation (Rahimzadeh et al. 2009; Darand et al. 2015; Soltani et al. 2016; Rahimi & Hejabi, 2018; Fallah-Ghalhari et al. 2019; Vaghefi et al. 2019) and the projected period (Darand, 2020; Naderi, 2020). As mentioned in the introduction, Iran stretched between 25 and 40° north and it does have mountain ranges such as Alborz and Zagros. It is evident that it experiences frost days (TN < 0 °C) in the cold period of the year (winter and autumn) and summer days (TX > 25 °C) in the warm period of the year (spring and summer). These two indices, also known as FD0 and SU25, are the leading indicators of ETCCDIs for temperature (Alexander et al. 2006), which investigated in most studies on an annual scale. Although these two indices and their changes are very important, it is clear that frosty days occur in mountainous areas and their existence is necessary even to eliminate pests in the cold period of the year and prevent extensive infestations. However, these two indices should be considered a risk when they occur on consecutive days and can be recognized as a severe risk by examining the maximum number of consecutive days. Accordingly, two new indices called the maximum number of consecutive frost days (CFD) and the maximum number of consecutive summer days (CSU) are used on a seasonal scale. The results of these two indices are widely used in various sectors, including energy, water resources, drought stress, optimal growth crops and frost damage, and transportation. Table 5 provides a complete explanation of these two new indices.

Table 5 Indices of maximum number of consecutive frost and summer days
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2.3.6 Theil-Sen’s estimator

The magnitude of trends in the WSDI and CSDI time series is estimated using the nonparametric Theil-Sen’s estimator (Theil 1950; Sen 1968) in Eq. (5):

$$\beta =median\left(\frac{{X}_{i}-{X}_{j}}{i-j}\right), \forall j<i$$
(5)

In the above equation, 1 < j < i < n is the estimator and β is the median overall combination of record pairs for the whole dataset.

3 Discussion

3.1 Minimum and maximum temperature validation of selected CMIP5 bias-correction models in Iran using the Taylor diagram

The Taylor diagram provides a statistical summary of the correlation between CMIP5 simulations and observation data in terms of correlation (R), a root mean square difference (RMSD), and the ratio of model variances (Taylor, 2001). Therefore, we used the Taylor diagram to investigate spatial distribution agreement between observation and CMIP5 simulation (Fig. 2). In the presented diagrams, the correlation between CMIP5 simulations for the minimum and maximum temperatures of Iran and observation is shown by the Azimuthal position from the test field. As mentioned, we have evaluated five climate models MIROC-ESM-CHEM, HadGEM2-ES, IPSL-CM5A-LR, GFDL-ESM2M, and NorESM1-M, from the CMIP5 bias-correction models. Then, the ensemble of these models is applied to study the seasonal ETI changes in Iran using the independence weighted mean (IWM) method. The validation results of 5 CMIP5 bias-correction models and the generated ensemble model by the IWM method showed that GFDL-ESM2M and HadGEM2-ES models represented the highest performance for the average of the whole of Iran. In contrast, NorESM1-M and IPSL-CM5A-LR models showed lower performance than other single models in Iran for minimum temperature (Fig. 2) and maximum temperature (Fig. 2), respectively.

Fig. 2
figure 2

Validation of CMIP5 bias-correction models in area-averaged of Iran using Taylor diagram for minimum temperature

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As shown in Fig. 2, the generated ensemble models using the IWM method have significantly reduced the bias compared to individual models in Iran. For example, as shown in Fig. 3 for maximum temperature, in autumn, the IPSL-CM5A-LR GCM has the weakest correlation and the GFDL-ESM2M GCM has the strongest correlation with 0.87 and 0.91 in the area-averaged for Iran. The ensemble model has increased the correlation to 0.96, which clearly shows how much the applying of the ensemble model decreases the bias in projecting future periods. The same is observed for the minimum temperature of autumn. The NorESM1-M model has shown the weakest correlation (0.86) for the minimum temperature. The GFDL-ESM2M model has shown the strongest correlation (0.91) among all.

Fig. 3
figure 3

Validation of CMIP5 bias-correction models in area-averaged of Iran using Taylor diagram for maximum temperature

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As shown in the diagram, the ensemble model with a correlation of (0.94) has dramatically reduced the bias. The same result is accurate for other seasons, which is also shown in the relevant diagrams. In many studies, the higher performance of MME compared to individual models is reported. For example, Reyers et al. (2016) examined 22 models in Europe and concluded that individual models for wind provide different results, whereas the ensemble model improves the performance. Also, the higher performance of ensemble models is approved in the Northeast China Plain with 28 global climate models (GCMs) for rice yield (Zhang et al. 2019), Peninsular Malaysia (Noor et al. 2019), global ETI of CMIP6 (Kim et al. 2020), Pakistan rainfall and temperature (Ahmed et al. 2020), and South Asia drought projection (Zhai et al. 2020). Therefore, the results represent that the minimum and maximum temperatures using MME models added a higher value to the output compared to applying individual models in Iran (Fallah- Ghalhari et al. 2019; Darand, 2020; Rahimi et al. 2020; Zamani et al. 2020; Naderi, 2020; Kamyar et al. 2020).

3.2 Seasonal variations of TN, TX, CSDI, WSDI, CFD, and CSU

Seasonal changes of six temperature indices studied in Iran during the historical period of 40 years (1965–2005) based on the output of CMIP5 MME models are shown in Fig. 4. Except for the TX and TN measured in degrees Celsius, four other indices represent duration, which measured in days. Our results show that the minimum seasonal temperature is at least − 5.53 and at most 28 °C in Iran. In summer, Dasht-e-Lut and Dasht-e-Kavir deserts are known as the main hot spots of TX and TN, with temperatures above 25 °C for minimum and more than 40 °C for maximum. In the other seasons, the primary sources of high temperatures for these two indices are southwest, south, and southeast of Iran. The reason for the very high maximum and minimum temperatures in the eastern half of Iran is the continental climate, being away from moisture sources, and various geographical features. Desert surfaces and clear skies, on the one hand, cause a significant increase in temperature, especially in the warm period of the year, and on the other hand, increase the coefficient of variation of temperature.

Fig. 4
figure 4

Long-term seasonal distribution of the ETIs (TN, TX, CSDI, WSDI, CFD, and CSU) during the historical period (1965–2005) in Iran based on CMIP5 output BC MME by IWM method. TN and TX units, (°C), CSDI, WSDI, CFD, and CSU units, (day)

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In winter (DJF) for both TX and TN indices, the temperature has an increasing gradient from northwest to southeast of Iran. In spring, the minimum temperature is − 0.55 °C, and the maximum temperature is 10.3 °C. In the northwestern and western regions, the maximum and minimum temperatures in spring are lower than in other regions of Iran. In this season, with the arrival of cold systems from the northwest and their rapid propagation in the northwest-southeast direction (location of the Zagros Mountain range) and finally, the accumulation of cold air due to the roughness of the Zagros Mountain range reduced the minimum temperature and maximized.

In summer (JJA), with the increase of day length in the northern regions of Iran, along with the increase of extensive subsidence of air, the temperature becomes more uniform, and the variability of minimum and maximum temperatures is less than other seasons.

The daily minimum temperature (TN) in summer is 8.37 °C, and the maximum value of the same index is 28 °C. For daily maximum temperature (TX), the minimum and maximum values are 25.6 °C and 44.8 °C, respectively. Atmospheric systems originating in the southern regions of Iran, such as Arabian anticyclone (Raziei et al. 2012) and subtropical high (STH) (Zarrin et al. 2010), are the leading cause of temperature increase in summer and play an essential role in increasing the maximum temperature in summer in southern regions of Iran.

According to the results of the five CMIP5 BC MME, the maximum temperature reaches 44.8 °C in summer in southwestern Iran. It should note that this value is the 40-year average of the maximum daily temperature. However, if its frequencies examine, the maximum temperature will be higher.

By comparing the figures of maximum temperature in spring and summer from south to north, we can see the impact of the northward movement of subtropical high pressure from spring to summer on temperature changes. In autumn (SON), the minimum temperature (TN) in the highlands of Iran has shown less than 5 °C. Changes in the minimum and maximum daily temperature range have shown that the temperature in Iran has many complexities and the interaction between local factors and atmospheric circulation systems cause many changes in the spatial patterns of temperature in Iran.

The study of changes in the two indices of TX and TN during the four seasons shows that they are the highest in all seasons on the southern coast of Iran. However, there is one exception in the summer, as the TX index does not show the highest values in the southern coasts of Iran in summer. It may be due to the establishment of subtropical high pressure (Zarrin et al. 2010) in boreal summer, which is located on the western and interior parts of Iran, and in terms of intensity and extent, it reaches its maximum value. Also, the transfer of humidity caused by the Asian summer monsoon (ASM) (Wang et al. 2015 and 2021) in southeastern Iran and the strengthening of sea breeze to land may be other factors that may cause the TX would be lower on the southern coast of Iran than the south west and interior region of the country. The WSDI and CSDI can be suitable indices for seasonal evaluating cold and heat waves during the historical period (1965–2005) using the output of MME (Fig. 4).

According to the description of the indices TX and TN, the two indices of WSDI and CSDI presented an utterly symmetrical pattern for Iran. Cold spells of Iran in winter vary between 1.32 and 4.09 days, and as expected, the western regions, the Alborz Mountain range in the north and northwestern Iran, showed the highest CSDI. Minimum CSDI is observed on the southern coast of Iran in all seasons.

The maximum value of the CFD index was seen in the highlands of northwest, west, north, and northeast. The maximum CFD in winter is 89.3 days, and the minimum index in terms of the seasonal cycle is observed in summer.

In spring, the maximum amount of CFD is limited to the northwest and highlands of Alborz in the north of Iran. The southern coasts do not experience CFD in any season. This index is limited to small parts of northwestern and western Iran in summer. Another index that has been used in this research for the first time on a seasonal scale is the CSU index, i.e., the maximum number of consecutive summer days. Except for a few limited areas on the Caspian coast, this index does not observe in winter above latitude 36° N. The Zagros Mountains are another area that does not experience CSU in winter. CSU index is mainly observed in winter on the coast of the Oman Sea by the maximum value of 20.8 days.

In spring, with increasing air temperature, the CSU value is 0.52 days in the northwestern, western, and northeastern regions of Iran. A maximum of 80.3 days was seen on the coast of the Oman Sea. In summer, as mentioned above, due to the subtropical high (STH) presence in most parts of Iran, the CSU reaches 92 days. In other words, except for northwestern Iran, which experiences only 25 days of CSU summer, all summer days in the rest of the country are associated with CSU.

In autumn, the CSU decreases sharply, and the index reaches 5.76 days. In contrast, summer conditions are still prevailing in the southern regions of Iran. The value of the CSU index in this region reaches 87.7 days, and the conditions of summer days observe in the coast of the Oman Sea to the Dasht-e Lut in central Iran and on the entire coast of the Persian Gulf.

3.3 The anomaly of projected CSDI

Projected changes in the CSDI in Iran for the near future (2021–2060) and far future (2061–2100) under the RCP4.5 and RCP8.5 scenarios have shown an utterly negative anomaly of the CSDI compared to the historical period (1965–2005). This decrease has already been confirmed by many studies examining Iran’s cold spells, such as Soltani et al. (2016) and Fallah-Ghalhari et al. (2019) which have been reported a decreasing trend for CSDI. CSDI negative anomaly is increasing from north to south and from east to west of Iran. The coasts of the Persian Gulf and the Oman Sea are the prominent hot spot of Iran’s cold spell in all seasons, periods, and studied scenarios. Based on projected results in winter (DJF), the CSDI in Iran will decrease between − 0.31 to − 2.88 days for the near future period (2021–2060) based on the RCP4.5 scenario (Fig. 5).

Fig. 5
figure 5

Seasonal distribution of projected anomalies of CSDI in Iran using ensemble CMIP5 models. Columns represent season and rows represent periods and scenarios

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In winter, the index has shown a 1-day increase for the minimum and maximum values in the far future compared to the near future period. Fallah-Ghalhari et al. (2019) also reported the increasing temperature trend. So that the minimum of the index with − 1.02 day and a maximum of that with 3.80 day decrease in future. The results of the RCP8.5 scenario also showed that the cold spells in the near future and the far future would decrease by a maximum of 3.34 and 4.09 days, respectively, in the winter.

In winter, the cold spells decrease for more than 2 days on the southern coasts of Iran. The minimum of cold spells anomaly was seen in the northeast, northwest, and east of Iran.

In the spring (MAM), future cold spell distribution showed that the coasts of the Persian Gulf and the Oman Sea had shown a decrease of more than 3 days in all periods for two scenarios. Similar anomalies were also observed in northeastern Iran in the spring (Fig. 5).

By the end of this century, based on the results of RCP8.5, cold spells in northwestern Iran have shown an anomaly of − 0.75, which does not reach even 1 day. Therefore, global warming will have the most negligible impact on northwestern Iran.

In the summer (JJA), the decreased trend of cold spells reaches its maximum magnitude. In this season, CSDI will decrease between − 2.05 and − 5.71 days compared to the historical period (1965–2005). The RCP8.5 result also showed minimum and maximum anomalies of − 2.23 and − 5.79 days. In the far future, the magnitude of negative anomaly would increase in the southern and southwestern regions of Iran. The eastern regions and the Alborz and the Zagros mountains range to experience the least negative anomaly of cold spells in Iran. The spatial pattern of CSDI anomaly in summer has shown that the coasts of the Persian Gulf are the prominent hot spot of this index in Iran. Unlike other seasons, in summer (JJA), Urmia Lake Basin has shown a significantly decreased trend for the CSDI. It is a severe threat to the ecosystems of Lake Urmia in the coming decades (Fig. 5).

In autumn (SON), CSDI has presented a homogeneous spatial pattern. So that below the latitude 35° N negative anomaly of cold spells reaches more than 2 days. By contrast, northwest Iran has shown the minimum anomaly of CSDI by 1 day/year (Fig. 5). In autumn (SON) and winter (DJF), the coasts of the Persian Gulf and the Oman Sea are the main hot spots of cold spell decrease in Iran. The decreasing CSDI in all seasons is a severe threat to water resources, agriculture, and pest growth.

3.4 The anomaly of projected WSDI

Investigating seasonal warm spells of Iran shows an increasing trend in the whole country under the projected scenario. Positive WSDI anomaly is increasing from north to south in Iran (Fig. 6).Identified areas that are the main hot spots of cold and warm spells showed that the decreasing cold spells in winter correlated well with increasing warm spells.

Fig. 6
figure 6

Seasonal distribution of projected anomalies of WSDI in Iran using CMIP5 bias-correction models, the ensemble models using IWM method. Columns represent season and rows represent periods and scenarios

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The results showed that warm spells in winter show a significant increasing trend, so it was expected that winters will be warmer in the coming decades. In the analysis of the mean time series of CSDI and WSDI, it was found that warm spells are more common than cold spells, especially in winter. Since CSDI and WSDI indices were computed from TX and TN temperature indices (10th and 90th percentiles), very hot days will be more frequent than very cold days in the future. In this regard, Im et al. (2017), by examining the heat waves of Asian countries, concluded that heatwaves would occur every 10 to 20 days at the end of this century and the coastal cities of southern Iran, Dubai, Abu Dhabi, and Doha are greatly affected by this event. They also showed that the wet-bulb temperature (TW) reached near 35 °C in the summer of 2015 in the port of Mahshahr (Iran), on the coasts of the Persian Gulf and in Saudi Arabia, indicating that the threshold broke earlier than expected (Schär 2016). Confirming the previous research (Schär 2016; Im et al. 2017), the results of our study showed the increase of thermal stress in the southern regions of Iran in the coming decades.

The anomaly of projected warm spells in winter (DJF), examined using the WSDI, has shown a significant increase over Iran. The anomaly hot spot of WSDI in winter is the coasts of the Oman Sea in southeastern Iran. Based on the RCP4.5 scenario, WSDI will have an anomaly of 3.24 to 16.4 days in the near future (2021–2060). While in the far future (2061–2100), the number of days will be doubled for warm spells, and according to the results of the RCP4.5 scenario, the maximum index reaches 35.5 days (Fig. 6).

The projected results using the RCP8.5 scenario show that warm spells will increase to a minimum of 4.22 days in the near future and 15.9 days in the far future. The maximum of 25.3 days and 64.6 days projected to increase in the near and far future, respectively.

In the spring (MAM), the warm spells projected a maximum increase of 59.8 days by the end of this century. In contrast to winter, when only the coasts of the Oman Sea showed the prominent spot of WSDI, in spring, the coasts of the Persian Gulf will also show a significant increasing trend. The northern regions, the northeast, and the northwest of Iran will experience a maximum increase of 14.5 days in the far future under the scenario RCP8.5 (Fig. 6). Warm spell events in the near future will increase by a maximum of 2 days compared to the historical period according to the RCP4.5 scenario.

In summer (JJA), we see a completely different spatial anomaly pattern of WSDI in Iran. In this season, the eastern regions of Iran and the northern and northwestern regions showed the most negligible increase in the frequency of warm spells. Unlike the CSDI, which showed the maximum negative anomaly on the coast of the Persian Gulf, this region is the primary hot spot of positive anomaly warm spells in Iran in this season. At the end of the century, under the RCP8.5 scenario, the frequency of warm spells will increase by about 80 days, a severe threat to the inhabitants of this region. In the far future (2100–2061), according to the RCP8.5 scenario, the frequency of warm spells will increase at least 41 days across Iran.

In the autumn season (SON), from the Strait of Hormuz to the west, we see severe anomalies of warm spells. This significant increase, based on the results of the RCP8.5, reaches 72.9 days in the period 2061–2100, which is 7.4 days longer than in summer. In this season, the northeastern regions and the southern coast of the Caspian Sea show the most negligible WSDI anomaly. The results showed that warm spells would increase in the future in terms of frequency and duration. In the cold seasons (winter and autumn), warm spells will have more intensity and frequency. In the southern coasts of Iran, warm spells are more persistent. The number of days with WSDI > 20, covers a smaller percentage of the area of Iran despite its significant intensity (Fig. 6). In contrast, the frequency of WSDI < 20 was seen in most parts of Iran. The frequency of warm spells is high in the southern, southeastern, southwestern, and central coasts of Iran.

The geographical distribution of warm spells in Iran showed that its hot spots were generally found in the southern regions of Iran, especially on the coast of the Persian Gulf and the Sea of Oman. Also, the increase of warm spells in the Zagros Mountain range is more than Alborz Mountain. This increase of warm spells is significant for the life of Iran’s main rivers, such as Karun, Karkheh and Zayandeh-Rud, which can pose significant threats to Iran’s energy (hydropower), agriculture, and water resources sectors. The rising temperature trend in the mountainous and snow-covered regions of the Zagros is larger than the northern regions of Iran, and their annual snow reserves will melt faster in the future. Globally (Pepin et al. 2015) as well as numerous regional studies (e.g., Andean Mountain range (Vuille et al. 2015) and Tibetan Plateau (You et al. 2018)), it showed that mountains are warming faster than the global average. In this regard, Fallah-Ghalhari et al. (2019) and Zarrin and Dadashi-Roudbari (2020) reported an increase in temperature across Iran, especially in the highlands of western and northwestern it, by the end of the century.

3.5 Seasonal projection of CFD in Iran

The projected changes of the CFD are shown in Fig. 7. The CFD index is a general indicator of frost damage. As mentioned earlier, for the historical period, all studies were conducted in Iran (Rahimzadeh et al. 2009; Soltani et al. 2016; Fallah-Ghalhari et al. 2019; Darand, 2020) used the FD0 index, which provided general information on changes in frost days throughout the year. The results of seasonal projection for the two periods 2021–2060 and 2061–2100 showed that the anomaly of CFD index is negative in all seasons of the year based on two scenarios, RCP4.5 and RCP8.5. Since there are more frosty days in winter, the anomaly of this index is more in this season.

Fig. 7
figure 7

Seasonal distribution of projected anomalies of CFD in Iran using CMIP5 bias-correction models, the ensemble models using IWM method. Columns represent season and rows represent periods and scenarios

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The CFD anomaly in this season is between − 0.03 to − 16.1 days/year−1 based on the results of the RCP4.5 scenario in the near future compared to the historical period (1965–2005). The maximum anomaly was observed in the interior mountain, Zagros, Alborz, and the northeastern mountain of Iran. In all seasons, the southern, southeastern, and southwestern coasts of Iran and most parts of central Iran show minimal CFD anomalies. The reason for this is either the lack of CFD during the historical period in seasons such as summer in large parts of Iran or that these areas did not have CFD in the historical period. According to the results of RCP4.5, the CFD index will decrease by a minimum of 1.1 and a maximum of 24.4 days in the far future. The maximum of this reduction anomaly was observed in Zagros Mountain. According to the RCP8.5 scenario, the index has decreased by 20.6 and 38.1 days for 2021–2060 and 2061–2100, respectively (Fig. 7).

In the spring (MAM), the results of the RCP4.5 scenario show that during two study periods, the CFD anomaly in Iran is a maximum of 10 days. The CFD will decrease by a maximum of 6.39 and 9.65 days in the western and northwestern highlands of Iran during the near and far future period. The central, eastern, and southern regions of Iran do not have consecutive frost days or very few in spring. The results of the RCP8.5 scenario for CFD in Iran showed a decrease of 15.7 days in the far future (Fig. 7). The result is consistent with previous studies (Fallah-Ghalhari et al. 2019).

In the summer (JJA), as mentioned, we see CFD in almost a few places in Iran. Therefore, large parts of Iran will not have CFD in the future. The western and northwestern highlands of Iran with 0.5 days are the only parts that show CFD anomalies in summer. The results for the autumn (SON) showed that CFD in Iran has an entirely decreasing anomaly like other seasons and especially in comparison with the winter (DJF). The significant CFD anomalies were seen in the Alam-Kuh highlands in northern Iran, Lalehzar in southern Iran, and Kuh-e Dinar in the Zagros Mountains. The maximum anomaly of the RCP4.5 scenario is 7.8 days, and the RCP8.5 scenario is 11.9 days (Fig. 7). In autumn (SON), except for the above-mentioned regions, the CFD anomaly is less than 5 days. The summary of the results of this section shows that the frost days and especially the maximum consecutive frost days in Iran will decrease in the coming years. This reduction was already reported by many studies examining Iran’s FD0; As Darand et al. (2015), using the Iranian climatic database during 1962–2004, also reported a decreasing trend for frost days. Also, Fallah-Ghalhari et al. (2019) reported a decreasing trend for frost days in Iran during 1976–2005 using the records of 45 ground stations in Iran, which confirms the results of this study.

3.6 Seasonal projection of CSU in Iran

Investigating the winter (DJF) consecutive summer days, it is found that CSU will experience a significant increasing trend on the coast of the Oman Sea in southeastern Iran during the two periods 2021–2060 and 2061–2100 under two scenarios, RCP4.5 and RCP8.5. Except for the region mentioned above, other parts of Iran have shown CSU anomalies of less than 10 days. The CSU maximum for the near future 2021–2060 is 12.7 days and is 26.4 days for the far future under the RCP4.5 scenario. It is 21.1 and 42.6 days for the near and far future under the RCP8.5 scenario, respectively. What is interesting is the significant increase in CSU in winter for the southern and southeastern regions of Iran. The maximum summer days of Iran in winter (DJF) are even longer than spring (MAM) and autumn (SON). In contrast, regions with increasing CSU longer than 10 days in spring and autumn are seen in more than 90% of the country (Fig. 8).

Fig. 8
figure 8

Seasonal distribution of projected anomalies of CSU in Iran using CMIP5 bias-correction models, the ensemble models using IWM method. Columns represent season and rows represent periods and scenarios

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In the spring (MAM), as shown in Fig. 8, the maximum CSU covers all areas below the 36° N, Unlike other seasons, the coast of the Persian Gulf shows the maximum CSU values. This result shows that the transitional seasons (spring and autumn) will disappear in the coming decades in the southern regions of Iran, and the summer season will be longer. Projections show an increase of at least 1.04 days and at most 28.6 days for CSU in Iran. The minimum anomaly of CSU was observed in spring in the northwestern regions of Iran (Fig. 8).

In summer (JJA), we see a different spatial distribution of CSU in Iran. In this season, the northwestern region experiences a positive anomaly of CSU. According to the results of the RCP4.5 scenario, summer days will increase by about 25 days in 2021–2060 in this region of Iran. At the end of the century, this index reaches 47.9 days, according to the results of RCP8.5 (Fig. 8). This unprecedented increase in CSU is a significant threat to Lake Urmia, which has been revitalized in recent years and may re-enter the landlocked period of this strategic lake in the not-too-distant future. On the other hand, this region is the agricultural hub of Iran, and the CSU index can provide valuable information for drought stress and optimal plant growth.

The autumn season (SON) has shown many changes compared to winter (DJF) and spring (MAM) seasons in Iran. In this season, the coast of the Persian Gulf in southwestern Iran and the coast of the Oman Sea in southeastern Iran show the minimum anomaly of CSU. This result is not far from the expectation because these areas are among the hottest areas of Iran with high CSU and according to previous findings (Zarrin and Dadashi Roudbari, 2020), with global warming, the temperature-based extreme indices will increase in Iran higher latitudes, especially in the mountainous regions of the country. Eastern regions, Central Iran, Zagros Mountains, and West and North-West of Iran show an increase of 10 to 27.8 days for this season in Iran (Fig. 8). This increase in the high single free-standing mountain of the Iran southern latitudes is a severe threat to water resources because as the temperature warms, we will see a decrease in snowfall, and also it is rapid melting in this region of Iran.

3.7 The seasonal anomaly of extreme temperature indices (ETI) in Iran

For a more detailed analysis of the six indices studied in Iran during different seasons, the anomaly of each index computed for the country-wide area-averaged, and its results are presented in Table 6. The results indicate that except for two indices, CFD and CSDI, which are representative of the maximum number of consecutive frost days and cold spells, other indices show positive anomalies for all studied seasons and periods. The TN index for the average of Iran reaches 0.43° in near future (2021–2060) and 7.60° in the far future (2061–2100) for winter (RCP4.5) and summer (RCP8.5), respectively. In other words, winter will have the lowest increase, and summer will have the highest increase for TN in Iran.

Table 6 The seasonal area-averaged anomaly of selected ETI indices of Iran based on CMIP5 BC MME results
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The results of the TX index are the same as TN. Our studies showed that the maximum daily temperature will increase between 1.66 and 6.11o by the end of the century. The anomaly of CFD would be negative for the country-wide average in the future. The cold seasons of the year (DJF and SON) show the most significant decrease in CFD.

In winter, according to the results of the RCP4.5 scenario, the value of CFD will decrease by 5.46 days in 2021–2060. According to the results of the RCP8.5 scenario, we will see a significant decrease of CFD by 13.43 days by the end of the century. The CSU index was also examined to understand better the effects of global warming on Iran’s climate. An interesting point for the CSU index is the increase in the anomaly of this index for the transition seasons of the year (MAM and SON). At the end of the century, under the RCP4.5 scenario, this index will increase by 11.35 days in spring (MAM) and 14.12 days in autumn (SON). According to the RCP8.5 scenario, the WSDI will be 18.79 days and 20.51 days in MAM and SON, respectively (Fig. 9). In other words, the spring and autumn seasons are shortening in Iran.

Fig. 9
figure 9

Long-term time series of CSDI and WSDI indices for area-averaged Iran based on CMIP5. The trend slope was calculated based on Theil-Sen’s slope estimator test

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In contrast, the length of summer is increasing (Fig. 9 and Table 6). The two indices CSDI and WSDI, which represent the cold and warm spells of Iran, also show the decrease of cold and warm spells. On a seasonal scale, Iran’s cold spells are decreasing at a rate of 3 days/season.

Iran’s warm spells also showed a significant increase in autumn (SON) and summer (JJA). The minimum increase in WSDI in winter with at least 7.22 days under RCP4.5 was observed in the near future (2021–2060). In contrast, the maximum WSDI with a maximum of 62.67 days will experience in the far future (2061–2100) under the RCP8.5 scenario (Fig. 9). Globally, many studies have reported an increase in temperature period indices and a decrease in cold and frost indices using CMIP5 models. Examples include research in the USA (Barnett et al. 2012), Mainland China (Ying et al. 2020), South Asia (Ullah et al. 2020), and the Middle East–North Africa (MENA) (Ntoumos et al. 2020). Therefore, it is acknowledged that global warming in Iran will be very intense in the coming years, and this increasing intensity will be significant for indices related to duration.

To better capture the long-term changes in ETI in Iran, CSDI and WSDI, the most essential and reliable indices for measuring the length of the hot and cold periods, were selected and the area-averaged trend examined across the country from 1965 to the end of the twenty-first century. The results showed that CSDI is decreasing with a very steep slope in all seasons of Iran and contrast, WSDI has a significant increasing slope in Iran. The trend slope is also calculated using the Theil-Sen estimate test for each season. For example, in the autumn season (SON), the CSDI in the historical period (1965–2005) shows a decreasing trend of 1.38 days/decade. In contrast, the WSDI increased by 0.48 days /decade in the same season. The most significant increase in the WSDI is related to the summer season (JJA), under the RCP8.5 scenario, which will increase by 8.77 days/decade (Fig. 9).

4 Conclusion

In this study, we examined the mean of daily minimum temperature (TN) and mean of daily maximum temperature (TX) of five models, including HadGEM2-ES, IPSL-CM5A-LR, MIROC-ESM-CHEM, GFDL-ESM2M, and NorESM1-M from CMIP5 bias-correction models on a seasonal scale.

Our results showed that GFDL-ESM2M and HadGEM2-ES models have the highest, and NorESM1-M and IPSL-CM5A-LR models have the lowest performances in simulating temperature in Iran. We put these five models together with the independence weighted mean (IWM) method, and we showed that multi-model ensembles (MME) in the country-wide average has a higher performance than individual CMIP5 models in all seasons.

The results of this study in applying CMIP5 models for TN and TX, on the one hand, and investigating seasonal ETI in Iran, on the other hand, have two significant advantages concerning other studies in Iran. Most studies of CMIP5 models in Iran have used the uncorrected biased output of these models (Zamani & Berndtsson, 2019; Abbasian et al. 2019; Rahimi et al. 2020; Zamani et al. 2020; Naderi, 2020; Kamyar et al. 2020). Few studies that have examined the climate extreme of Iran with CMIP models rely on the output of individual models that has definitely with high uncertainty (Roshan & Nastos, 2018; Katiraie Boroujerdy et al. 2019; Darand, 2020; Sharafati & Pezeshki, 2020).

The results showed that the frequency and duration of the CSDI period under RCP4.5 and RCP8.5 scenarios decrease in Iran. In contrast, the duration of warm spells increases, significantly increasing the health risks of heatwaves in Iran. Globally, increasing the frequency of high-temperature extremes and decreasing the frequency of low-temperature extremes have also been approved by Min et al. (2013). The results of the present study also confirm it. At the end of the present century, under the RCP8.5 scenario, the WSDI has shown a 62.6 day increase in summer, while the CSDI decreases by a maximum of 3.43 days compared to the historical period.

Significant reduction of cold spells may negatively affect the health of Iranian society and natural ecosystems. In this regard, Diffenbaugh et al. (2008) showed that lowering the minimum temperature increases the growth of pests.

The WSDI will significantly increase in Iran under RCP4.5 and RCP8.5 scenarios. The WSDI anomalies increase on the coasts of the Persian Gulf and the coasts of the Sea of Oman by the end of the century under the RCP8.5 scenario. The WSDI anomalies include 72.9 days in autumn, 64.6 days in winter, 59.8 days in spring, and 80.3 days in summer compared to the historical period (1965–2005).

Global warming has not only increased the minimum (TN) and maximum (TX) temperatures in Iran; it also increases the consecutive periods of high-temperature extreme events (e.g., WSDI and CSU). The minimum temperature will increase from 0.43 to 7.60°, and the maximum temperature will increase from 1.66 to 6.11° across Iran on a seasonal scale.

In this regard, Zwiers et al. (2011) confirmed the increase in global minimum and maximum temperatures. Almost no cold spell can be detected in Iran under the RCP8.5 scenario in the far future (2061–2100). Significant decrease in the CSDI and increase in the WSDI are not only seen in Iran but also in some areas such as China (Chen & Zhang, 2016), nine major basins in China (Xu et al. 2019a, 2019b), and even globally (Lu et al. 2018). These extensive changes are also reported using CMIP5 models and more recently with CMIP6 models (Kim et al. 2020).

The CFD and CSU indices, which depicted the highest consecutive days of frost and summer days in Iran, showed that the CFD (CSU) would decrease (increase) in the future under the scenarios of RCP4.5 and RCP8.5. The highest decrease of CFD is in winter (DJF) by an average of 13.49 days in 2061–2100 under the RCP8.5 scenario. The autumn has the second-highest decrease in CFD in Iran.

The maximum consecutive summer days are in autumn with 20.51 days and then in spring with 18.79 days. Our results show that summer days are increasing, and the length of spring and autumn seasons will be shorter at the end of this century. In contrast, the summer season in Iran will expand by the end of the century. The frequency of summer days will increase by 42.25% in Iran under the RCP8.5 scenario. The results obtained in this study for increasing the minimum and maximum temperatures have been reported by Ghalhari and Roudbari (2018), Fallah-Ghalhari et al. (2019) and Ahmadi et al. (2021) as well as increasing the average air temperature by Zarrin and Dadashi-Roudbari, (2020). Also, Darand (2020) showed the minimum of the daily minimum temperature (TNn) and the minimum of the daily maximum temperature (TXn) will increase in the future. In this regard, increasing WSDI and decreasing CSDI for the observation period using Iran meteorological stations have been previously confirmed (Rahimzadeh et al. 2009; Soltani et al. 2016; Fallah-Ghalhari et al. 2019).

In general, it seems that under the conditions of future climate change, planning should be subject to taking into account the above conditions, including a decrease in the number of frosty days and a significant increase in summer days. The results of this study are of great importance in the planning of energy systems, agriculture, and water resources management. It is suggested that in the future research, the recently published models of the Coupled Model Intercomparison Project Phase 6 (CMIP6) be used and the results be compared with this work.