1 Introduction

Climate change is a serious global challenge for the sustainability of water, energy and ecosystem processes and has very serious effects on the hydrological cycle. It is the result of the population growth, increased fossil fuel utilization, soil erosion deforestation and, hence, increased greenhouse gases (Li et al. 2016; Pachauri et al. 2014; Liu and Merwade 2018; Ashofteh et al. 2015a, b, 2017; Azadi et al. 2019; Liu et al. 2021). Studying the climate change parameters plays an important role in forecasting surface runoffs to identify and manage the water resources because climate change changes the rivers’ hydrological regimes and, hence, the frequency and severity of floods making it necessary to study hydrological processes required for making environmental management decisions, allotting water resources, protecting rivers’ ecosystems and restoring rivers (Chu et al. 2013; Sharifi et al. 2017; Chen et al. 2019). The main source of water demand is the runoff created by streams (Ercan et al. 2020). If water resources are not available there will be hydrological drought resulting in severe effects such as: (1) deteriorated water quality, (2) crop failure due to limited irrigation water, (3) reduced electricity generation, (4) disrupted river habitats and (5) limited recreational/economic/social activities (Mishra and Singh 2010).

Since this source does not sufficient, and the available fresh water resources are limited, water shortage will become a major future problem of the human societies. Therefore, more accurate prediction of the discharge and its variations during the year is a basic step in the planning and management of surface water resources (Shaigan et al. 2011). Naturally, since climate change affects runoffs, the hydrological drought index will also change in the future; in other words, the reduced runoff will increase the future drought periods and severity. Among researchers who have studied the drought index in previous periods, Babaeian et al. (2021) introduced a combination of adaptation pathway (AP) approaches that were used in conjunction with the SWAT model to evaluate the resilience of adaptation measures and design robust adaptation pathways taking into account the future climate uncertainty in the Hablehroud River Basin. Salimi et al. (2021) studied the effects of the climate change on hydrological and meteorological droughts. They used Standardized Rainfall Index (SPI), SPEI and Standard Stream flow Index (SSI) in the Navrood and Lighvan watersheds in north of Iran and observed high correlation between hydrological and meteorological droughts. Also, they concluded that the climate change was the most effective factor in the occurrence of future droughts. Abdulai and Chung (2019) studied the meteorological and hydrological droughts caused by the climate change under the RCP4.5 scenario in the Cheongmicheon watershed in South Korea. Their results referred to the occurrence of short-term severe or extreme droughts according to the standardized rainfall evapotranspiration index (SPEI) and streamflow drought index (SDI). Kamali et al. (2017) examined the climate change in the Karkheh river basin. They used the SWAT distribution hydrological model for runoff projection. They proposed the Drought Hazard Index (DHI), which is a combination of meteorological, hydrological, and agricultural droughts, and their results indicated the occurrence of drought based upon the DHI index. Studies conducted, so far, on the climate change effects on basins’ runoffs include those of Xue et al. (2021), Kiprotich et al. (2021), Su et al. (2021), dos Santos et al. (2021), Chang and Su (2021), Lian et al. (2021), Li et al. (2021), Escanilla-Minchel et al. (2020) and Ridwansyah et al. (2020), just to mention a few.

Studying the effects of the climate change on runoff requires the latter to be simulated by hydrological models which are accurate tools necessary for the sustainable use of water resources and studying hydrological processes (Abbaspour et al. 2015). A comprehensive, accurate hydrological model available for studying the hydrological and biogeochemical effects of the climate change is the Semi-Distributional Soil & Water Assessment Tool (SWAT) which is an integrated, complex, basin-scale model capable of analyzing data annually, monthly, daily and hourly (Arnold et al. 1998). It was first presented by Dr. Jeff Arnold (Arnold 1994) for the United States Agricultural Research Service to predict the effects of management practices on water, sediment, and so on in large and complex basins with different land uses (Arnold et al. 1998; Shaigan et al. 2011; Neitsch et al. 2011).

To date, several studies have used SWAT to investigate runoffs; Alansi et al. (2009) used it to simulate runoffs to study the land-use variation effects upstream of Bernam basin in Malaysia. They used R2 and Nash-Sutcliff (NS) impact coefficients to evaluate the simulated model and showed, through their results, that SWAT was highly capable of simulating and predicting runoff flows under humid tropical conditions.

Goyal et al. (2018) used SWAT in different DEMs to simulate runoff and sediment of the Narmada and Teesta fall basins in India and showed that different DEMs did not have meaningful effects on runoff results while their effects on the sediment simulation results were significant. Kaffas et al. (2018) used the Composite Mathematical Model (CMM) – Arc SWAT composite mathematical model for the modeling of hydro morphological processes in the Nestos river basin with an area of 840 km2 in the mountainous part of Greece. They measured the discharge and sediment rates by SWAT and CMM methods and showed that composite model modeled sediments less accurately than CMM, but simulated runoffs satisfactorily. Aiming at investigating the effects of climate on runoff, flood and drought downstream of Kan semi-arid watershed, west of Tehran, Ahmadi et al. (2019) used ANN, SWAT and IHACRES used ANN, SWAT and IHACRES to simulate rainfall and runoff under daily, monthly and annual scale for the period of 1987–1995. They suggested ANN and IHACRES because the basin lacked information and recommended SWAT for studying floods, runoffs and basin’s physical properties. Chen et al. (2019) examined the effects of parameter uncertainty and structure of hydrological models in daily, monthly and annual land-use variation studies and simulated the Xitiaoxi Basin runoff in China using SWAT and HSPF hydrological models; the HSPF showed more monthly and annual runoff variations than SWAT. Differences in hydrological simulations could have been due to different equations used for both models. De Andrade et al. (2019) used SWAT to simulate the soil moisture and runoff in Brazil’s northeastern basin. They examined the related uncertainty data in hydrometric stations and found NS coefficients of 0.71–0.92 and 0.53–0.76 for annual calibration and validation and 0.55–0.78 and 0.62–0.72 for monthly calibration and validation, respectively. Predicting the river discharge, where rainfall and air temperature are vital parameters, is an important issue in water resources engineering as regards the resource planning; in other words, the surface runoff discharge can be predicted by predicting the air temperature and rainfall (Khazaei and Mirzaei 2013) one method for which, for future time periods, is using statistical exponential micro-scale models. Some of the studies conducted, so far, on the effect of climate change on basins’ runoffs using the predictions of exponential micro-scale models and simulations of the SWAT model are as follows: Liu et al. (2020) used SWAT to study the effects of climate change on the surface water in the South-Central Valley, California, for the year 2020. In this study, they used four climate models (HadGEM-ESCMIP5, CNRM-CM5, CanESM2, Miroc5) and two emission scenarios (RCP4.5, RCP8.5) and showed, by their results, that the peak river flow was expected to increase 0.5–4 times in the coming decades under warm weather conditions and occur 2–4 months earlier in the year due to snow melting. They also concluded that in the near future (by the end of the twenty-first century), the snow cover would gradually decrease with lower rates at lower altitudes and with higher rates at higher altitudes. According to their predictions, the surface water would increase in the Valley, but increased time variations (more wet seasons and drier dry seasons) would cause new challenges for the supply management. They further emphasized that the remote measurement-based snow water equivalent (SWE) data could fill the current gap of the SWE observations in a limited area to improve the Swat snow setting and better predict the climate change effects in semi-arid and snowy watersheds. Tan et al. (2017) used CMIP5 and SWAT models to study the Kelantan River catchment area in Malaysia. In this study that included 36 micro-scaled weather forecasts from 5 general circulation models (GCMs) under 3 RCP scenarios (2.6, 4.5, 8.5) in the SWAT calibrated model for the 2015–2044 and 2045–2074 periods, they showed that monthly rainfalls increased during wet seasons and reduced during dry seasons concluding that the monthly surface flows were likely to increase in November, December, and January and reduce slightly between June and October during the 2015–2044 period. These findings can serve as a scientific reference to develop better climate-adaptation strategies. Using a set of CMIP5 GCMs, Wodaje et al. (2021) evaluated the climate-change uncertainty effects on the Bilate River flood flow, Ethiopia, SWAT-simulated the water flow and showed, statistically, that the model predicted the flow logically. The annual discharge increased considerably for all time periods throughout the century; the flow increases under RCP8.5 scenario (compared to RCP4.5) was nearly 42.42% during the 2080 period. Andrade et al. (2021) used SWAT, two RCMs (Eta-Miroc5, Eta-HadGEM2) and two scenarios (RCP4.5, RCP8.5) to evaluate the future climate-change effects on Mundaú River Basin water resources, Brazil, for three time periods and showed, by climate models’ predictions, that, in general, the Mundaú River Basin would experience significant annual rainfall reductions of between 0.4% (1,087.45 mm) and 25.3% (815.59 mm) in both scenarios, respectively.

Studies conducted so far on the effects of climate change on runoffs in mountainous basins are limited; however, none has addressed the prediction of the hydrological drought index in these basins. Therefore, this research is aimed to study the effects of the climate change on runoffs, evaluate the hydrological drought index and examine the flow trend in the Alvand mountain basin in Iran. To this end, SWAT and CMIP5 climate models were used to simulate the basin runoff and predict the climatic parameters, respectively. This study is mainly aimed to: (1) calibrate SWAT and do a daily-monthly runoff comparison of 4 hydrometric stations in the Alvand mountain basin, (2) predict the temperature and rainfall in 2020–2040 period in five meteorological stations and (3) simulate the runoff of four stations using the predicted data and calibrated parameters and compare the observed runoff with that predicted for future periods, (4) investigate the runoff trend using Mann–Kendall method and (5) evaluate the future hydrological drought index and compare it with that of the past.

2 Materials and methods

2.1 The study area

The Alvand mountainous basin, is located in Hamedan province and a sub-catchment area in the western part of Iran, which is formed along with the Zagros Mountain range, and its other name is Central Zagros with an area of 1133.62 km2 along the longitude 48◦36′to 48◦7′North and the latitude 34◦28′to 34◦56′East. The minimum altitude in this area is 1582 and the maximum altitude is 3555 m above sea level Fig. (1).

Hamedan synoptic stations have reported 8.36, 6.9 and − 6.29 °C for, respectively, the absolute maximum, average and absolute minimum air temperature in the Alvand mountain basin; the warmest months are July and August (maximum 35 °C) and the coldest are January and February (average − 4.25 °C). Reports also show that the annual rainfall is more than 300 mm varying in different months with a maximum of 95 mm in April, 82 mm in May and 81 mm in June, and varying seasonally in other months (http://www.irimo.ir).

2.2 SWAT model

To simulate the runoff flow, this study has used SWAT which is a semi-distribution physical hydrological model designed to predict long-term runoffs, sedimentations and chemical-agricultural products in a watershed. It does the simulation of hydrological processes in two phases: (1) ground or soil profile and (2) routing, respectively (Arnold et al. 1998). Phase ground calculates the inflow of water, sediments, nutrients and pesticides to the main channel in each reservoir based on the water balance concept that considers such important processes as rainfall, ET, seepage, surface runoff, lateral flow and groundwater flow, and phase routing uses the main channel to connect all sub-basins and simulates the water and sediment movement towards the basin outlet (Cibin et al. 2010; Chen et al. 2019; Arnold et al. 1993; Gebremariam et al. 2014). In SWAT, interflow is calculated using a linear function that consists of slope length and angle, saturated conductivity, drainable porosity and the amount of water that is stored in the saturated zone (Cornelissen et al. 2013). SWAT simulates hydrological cycles based on the following water balance Eq. (1):

$$ {SW}_{t} = {SW}_{0} + \sum {\left( { R_{day} - Q_{surf} - E_{a} - W_{seep} - Q_{gw} } \right)} $$
(1)

where SW0 and SWt (mm) are the initial and final soil water and Rday, Qsurf, Ea, Wseep and Qgw (mm) are the rainfall, runoff, ET, water seepage to the upper soil layer and return flow in the ith day, respectively.

2.3 SWAT input data

SWAT uses the digital elevation model (DEM) and Raster primary functions through the Spatial Analyst feature in the ArcGIS software to design flow networks and basin boundaries (Abbaspour et al. 2007). To this end, the DEM10 map was first obtained from the Natural Resources Department (Section of Studies), Hamedan Province, and then used for modeling purposes (Fig. 2a). As the network of waterways and sub-basins was not previously identified, we formed it by the “flow direction and accumulation” technique and then examined it in the Google Earth software (Fig. 2b). This network and its basins were divided into 74 sub-basins (Fig. 2c). Since the provincial soil map did not exist, use was made of a global soil map and the land use map (Fig. 2d) was obtained from the mentioned Unit and introduced to the model in the GIS.

Fig. 1
figure 1

The site Location of Alvand mountain basin, Iran

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Fig. 2
figure 2

a Digital elevation model of the study area, b Hydrometric stations and flow direction, c Division of Sub-basins, d Land use map

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Characteristics of the measuring stations of the meteorological and runoff parameters in the study basin are listed in Table 1. In this catchment, there were two synoptic stations, Hamedan and Tuyserkan, that used the daily data on radiation, rainfall, air humidity, wind speed, and air temperature in the 2003–2017 period, and five hydrometric stations (Fig. 2b), Ekbatan, SalehAbad, Maryanaj, Pole Aliabad, and TaghsimAb, with the daily information in the same period obtained from the Water Resources Department; although Ekbatan Station was not inside the study area, its daily rainfall data were used because it was quite close to the area. Data introduction to the model should be regular with no blanks or else the model will become erroneous; here, the model received 65,700 meteorological data.

Table 1 Specifications of the stations used in the area
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Performance of the mentioned model was studied and compared using such coefficients as: (1) Correlation, (2) NS, (3) PBIAS and (4) RMSE (Liu et al. 2021).

2.4 Future climate scenarios (climate forecast data)

To assess the climate change effects on runoffs as well as on the hydrological drought, the Lars-wg6 model was used to downscale and generate future daily rainfalls and temperature data through different general circulation models (GCMs). Two scenarios (RCP4.5 and RCP8.5) and 4 CMIP5 models (GFDL-CM3, Ec_Earth, Hadgem2_ES and Miroc5) were used to evaluate and model the rainfall and temperature of the 5 meteorological stations. While the first three represented the “average temperature and rainfall”, “cold and humid climate” and “hot and dry climate”, respectively, all 4 covered the CMIP5 model forecast results (Table 2).

Table 2 Specifications of 4 models selected from the CMIP5 collection for the present study (IPCC 2013)
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Each CMIP5 model considered varying emission rates of solar greenhouse gases, human activities, volcanic eruptions, emission of short-term species, and natural/human aerosols known, also, as RCP-representing concentration routes. This study considered RCP4.5 and RCP8.5 emission scenarios of each CMIP5 model both of which are commonly used by researchers because RCP4.5 is an intermediate scenario while RCP8.5 is generally considered as the worst climate-change scenario (Liu et al. 2021). In short, to estimate the future runoff in SWAT, the mentioned models and scenarios.

2.5 Mann–Kendall trend test

In this study for investigate the trend of runoff Mann–Kendall test was used. The Mann–Kendall method explained briefly next.

In the MK (denoted by MK1) test, the first step is the calculation of the S statistics using the observations and employing the following Eq. (2) (Mann 1945; Kendall 1975):

$$ Z = \sum\limits_{i = 1}^{n - 1} {\sum\limits_{j = 1}^{n} {{\text{sgn}} (x_{j} - x_{i} )} } $$
(2)

where xj is the value of jth data, n is the number of data, and sgn (θ) is the sign function, which is defined as:

$${\text{sgn}} (\theta ) = \left\{ {\begin{array}{*{20}l} 1 \hfill & {if} \hfill & {\theta \rangle 0} \hfill \\ 0 \hfill & {if} \hfill & {\theta = 0} \hfill \\ { - 1} \hfill & {if} \hfill & {\theta \langle 0} \hfill \\ \end{array} } \right\} $$
(3)

If n > 8, the S statistics has a normal distribution having E(S) = 0 and following variance:

$$ V(s) = \frac{{n(n - 1)(2n + 5) - t_{i} (t_{i} - 1)(2t_{i} + 5)}}{18} $$
(4)

where ti is the number of observations in the ith tied class, and m is the total number of tied classes. The score of MK test or Z statistic is calculated as follows:

$$ Z = \left\{ {\begin{array}{*{20}l} {\frac{S - 1}{{\sqrt {V(s)} }}} \hfill & {if} \hfill & {S\rangle 0} \hfill \\ 0 \hfill & {if} \hfill & {S = 0} \hfill \\ {\frac{S + 1}{{\sqrt {V(s)} }}} \hfill & {if} \hfill & {S\langle 0} \hfill \\ \end{array} } \right\} $$
(5)

If the (−Z1−α/2 ≤ Z ≤ Z1−α/2) condition is satisfied, H0 (null hypotheses) is accepted, which means there is no significant trend in the tested time series; otherwise, H1 (alternative hypothesis) is accepted, which means there is a significant trend in time series at α significance level.

2.5.1 Sen’s estimator

In this study, the magnitude of trends is calculated using the Sen’s estimator (Theil 1950; Sen 1968) method using the following Eq. (6):

$$ \beta = Median\left( {\frac{{ x_{i} - x_{j} }}{i - j}} \right)\quad \forall _{j} \langle i $$
(6)

where xj and xi are the jth and ith observations in the tested time series. The positive values of β represent the upward trends, whereas the negative values indicate the downward trends.

2.6 The streamflow drought index (SDI)

For determination of the severity and weakness of hydrological drought, an index similar to standardized rainfall index (SPI) called streamflow drought index (SDI) is used. This index is based on the monthly standard normal flow and was first introduced by Nalbantis and Tsakiris (2009). In the present study, SDI was calculated using a method completely similar to SPI (McKee et al. 1993). Therefore, for calculating this index, the same calculations were made except that discharge monthly series were used instead of rainfall data as the input. Accordingly, first, the time window was introduced for the monthly series of river discharge. The time window shows the multi-monthly cumulative value of the river flow discharge. For example, the 3-month time window of June-2014 is the cumulative value of the streamflow values of the months April, May, and June of 2014 or the 12-month time window of June-2014 is the monthly cumulative streamflow values of July-2013 to June-2014. A cumulative monthly time window is derived based on the following equation:

$$ V_{i,k} = \sum\limits_{j = 1}^{3k} {Q_{i,j} ;} \quad i = 1,2,\ldots;\quad j = 1,2,\ldots12;\qquad k = 1,2,3,4 $$
(7)

where Vi;k is the cumulative streamflow value of the kth monthly period in ith hydrological year, j denotes the month within the hydrological year and Qi;j is the monthly streamflow (Myronidis et al. 2018; Tabari et al. 2013). After this step, by comparing different probability distributions, the fittest distribution was applied on the data in each of the time windows and the probability corresponding to each average discharge value was calculated. Subsequently, based on the principle of distribution transformation, the mentioned probability was transformed into standard normal distribution and new series of data were obtained that had a standard normal distribution with a mean of zero and a variance of 1. The SDI calculation

$$ SDI_{i,k} = \frac{{v_{i,k} - \overline{{v_{k} }} }}{{s_{k} }} $$
(8)

where \(\overline{{v}_{k}}\) and Sk are the mean and standard deviation of the cumulative streamflow volumes, SDIi;k is the value of streamflow drought index for kth monthly-based time window (Malik et al. 2019; Borji et al. 2016). According to Table 3, the severity and weakness of hydrological drought (or wet) condition, can be classified in the resulting series.

Table 3 Classification of hydrological drought severity for stream flow Drought Index
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The present study’s general flowchart is shown in (Fig. 3).

Fig. 3
figure 3

The proposed modeling framework

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3 Result

3.1 Calibrated parameters

The calibration step of a hydrological model is subjective and no automatic algorithm can replace the researcher’s knowledge in relation to their study area. Therefore, the calibration procedures and uncertainty analysis are closely connected, and no calibration should be performed without quantifying the degree of uncertainty associated with the model prediction (Abbaspour et al. 2015; de Andrade et al. 2019).

This study has used period of 2003 to 2008 as the Warm up period (because these 6 years had high positive effects on the authors’ statistical results), 2009–2014 for calibration and 2015–2017 for validation. As the study basin was mountainous and obtaining results was quite difficult, input parameters were considered separately for each sub-basin, which were totally 74 and similar ones were placed in one direction so that instead of setting one parameter for every sub-basin and finding an optimal value for it, only one was obtained for similar sub-basins that were totally 12; same was repeated for the soil map. Parameters used to simulate monthly and daily runoffs, their description and their calibrated values are listed in Table 4.

Table 4 SWAT model parameters’ calibrated and adjusted values
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In the present study, the Alvand mountain basin has 6 types of land use, and 3 types of soil. In this range, the hydrological group of the basin soils is in the B and C groups according to the soil permeability, i.e. the permeability of the range is between 3.8 to 7.5 (mm per hour). Besides the characteristics of the basin's surface cover are arable lands, grasslands, gardens or forests, there are also unused areas which are bare, urban, rocky and mountainous. In our study, the calibrated value of the curve parameter (CN) for 12 similar sub-basins ranged from 35 to 98, where high CN values show the low permeability of the soil and therefore more runoff. Parameters obtained in this basin show different soil types and land uses. While this calibration results for the CN parameter is consistent with those of Lin et al. (2014), the related values obtained in de Andrade et al. (2019), Zettam et al. (2017) and Hammouri et al. (2017) studies ranged from 35 to 98. The value of the Baseflow alpha-factor (ALPHA_BF) varied from 0 to 1 day, with a calibrated value of 0.040, which was consistent with the results of de Andrade et al. (2019) and Fereidoon et al. (2019). Groundwater delay time (GW_DELAY) can vary from 0 to 500 days, which is the default limit provided by the SWAT model. In this study basin, the calibrated value (with 1333.62 km2) was approximately 35 days, while de Andrade et al. (2019), recorded 135 days in the Mundau´ River basin (with an area of 4090.39 km2), as well as Xue et al. (2014) in China (with an area of 8,102 km2) obtained a calibrated value of 101 days whilst analyzing the surface current uncertainty parameter and sediment production in the Huolin Basin. On the other hand, Blainski et al. (2017) recorded a value of 0.65, indicating that the time interval required for underground feeding in the Camboriu´ River Basin (195 km2) was less than one day. These differences emphasize the significant role of drainage zone size in the GW_DELAY parameter. The water depth in shallow aquifers required for return flow (GWQMN) can vary from 0 to 5000 mm. The return flow from groundwater is related to rainfall and particularly evapotranspiration, since it is strongly dependent on capillary flow. A calibrated value of 239.9 mm indicates that the water level must be equal to or greater than approximately 0.24 m in depth for the return flow in the catchment areas of the region. de Andrade et al. (2019) obtained the GWQMN parameter value of 2686 mm.

The HRU_SLP (Average slope steepness) calibration mean value of was 1.61 in this study, which was essentially 61% of the initial value of each subset. The permissible value of RCHRG_DP deep aquifer percolation fraction varies between 0 and 1%. Its calibrated value for the total sub-basin is 0.9 Fereidoon et al. (2019) obtained the RCHRG_DP value in the Karkheh Basin of Iran between 0.25 and 0.64. Bhatta et al. (2019) obtained this value in the Tamor River Basin in Nepal 0.56. The Average slope length of the SLSUBBSN slope is between 10 and 150, and in this study, it was 94.42. Surface runoff lag time coefficient (SURLAG) can alter from 1 to 24, the calibrated value in this area was 12.985. Semiromi and Koch (2019) obtained the SURLAG value in the Gharehsoo River basin in Iran at 3.63. Bhatta et al. (2019) obtained this value in the Tamor River basin in Nepal 0.56. Aliyari et al. (2019) obtained the calibrated amount of SURLAG for the Pallet River Basin in Colorado at 6,985. The calibration value of the manning coefficient (CH_N2) was 0.062 in this study, which shows the effluents in the heavy clay-silty soil are almost uniform with the floor and the cross section of the effluents (Chow and Patterson 1959). de Andrade et al. (2019) found the calibration value of CH_N2 to be 0.34, and the main features of this channel are very grassy, torrential streams with heavy wood and plant bases. Rajib et al. (2016) found adjusted values CH_N2 from 0.02 to 0.15 in the studied basins. Zhang et al. (2015) obtained this parameter in the Jinjiang River Basin in China at 0.03. Pereira et al. (2014) obtained the CH_N2 value of the Headwater basin in southern Brazil at 0.011. The calibrated value of the CH_K2 Effective hydraulic conductivity in main channel alluvium in this study was 67.57.

For calibration of the Available soil moisture capacity (SOL_AWC), values can vary from − 60% to + 60%. This value varies from 0.04 to 0.12 mm/mm for different soil types. The calibrated value of SOL_AWC for the 5 similar sub-basins decreased from + 58% to − 13%. The highest is between 0.063 mm/mm and 0.19 mm/mm and the lowest is between 0.0348 mm/mm and 0.1044 mm/mm.

de Andrade et al. (2019) indicated that the SOL_AWC value for all soils between 0.053 mm/mm and 0.158 mm/mm. Aliyari et al. (2019) obtained the calibrated value of SOL_AWC for the Pallet River Basin in Colorado at 0.9136. Chen et al. (2019) obtained the calibrated value of SOL_AWC between 0.025 and 0.35. The calibration value of saturated hydraulic conductivity (SOL_K) in this study was between 123.68 and 1159.6 for pasture and basin coverage. According to Andrade et al. (2013), saturated hydraulic conductivity usually presents a high spatial variability, and the SWAT model does not take into account this spatial distribution but, rather, a mean value for a given soil type. Then, the model provides, from the optimization process, the maximum value allowed in the calibration step.

The Moist bulk density (SOL_BD) varies from − 50% to + 50%. This amount has increased to 222 percent for the same 5 sub-basins and also decreased to 14 percent. Fereidoon et al. (2019) obtained SOL_BD values in the Karkheh basin of Iran between 0 and 0.23.

3.2 Calibration and validation of SWAT

Comparison between the simulated and observed hydrographs is an important procedure to evaluate model calibration (Andrade et al. 2013; Blainski et al. 2017). Figures 4 and 5 show the hydrographs observed and simulated by the SWAT model, in the calibration and validation phases, for the four streamflow gauge stations of the Alvand mountain Basin (SalehAbad, Tooijin, TaghsimAb and Pole Aliabad) for daily and monthly time steps, respectively. For both time steps, a satisfactory fitting between measured and simulated hydrographs was observed. The model has simulated the studied area well, but has been relatively erroneous in simulating the runoff peak.

Fig. 4
figure 4

Comparison of the simulated daily runoffs with those observed in SalehAbad, TaghsimAb, Maryanaj and pole Aliabad stations

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Fig. 5
figure 5

Comparison of the simulated monthly runoffs with those observed in SalehAbad, TaghsimAb, Maryanaj and pole Aliabad stations

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Table 5 shows the comparison among the statistical indicators (R2, NS and PBIAS) for discharge calibration and validation using the SWAT-CUP semiautomatic calibration method. Values of R2 ranged from 0.48 to 0.76 for daily and monthly flow calibration, and from 0.38 to 0.70 for validation; as shown, the difference between the two is not much. The NS coefficient ranged from 0.4 to 0.7 for monthly calibration and from 0.4 to 0.52 for daily calibration; the reason for less daily accuracy factor than monthly is that the data calibrated daily at each station are 2922, but for the monthly case they are 96. According to the NRMSE coefficient that shows the percent error, the highest calibration and validation error rates are, respectively, 17.5 and 19.7% for the monthly data of the TaghsimAb, and the lowest are, respectively, 8 and 48.47% for the daily data of Maryanaj station. These results show that, in general, the SWAT performance is good and satisfactory for rivers flowing from the Alvand mountain basin based on Moriasi et al. (2007) proposed classification.

Table 5 A summary of the daily and monthly time step calibration and validation of the SWAT model statistics in the four streamflow gauge stations of the Alvand mountain basin
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3.3 Evaluating the rainfall and temperature parameters and simulating the future runoff

The statistical data, including the daily rainfall for Hamedan, Tuyserkan, SalehAbad, Maryanaj and Ekbatan stations and the minimum and maximum temperatures for Hamedan and Tuyserkan stations were gathered in period of 2003 to 2017, then used as input Lars-wg model to simulate future rainfall and temperature based on the CMIP5 models for period of 2020 to 2040.

Table 6 lists the R2, NS, PBIAS, RMSE and NRMSE error criteria for the selected models. The results show that Miroc5, with the lowest error, is the best model to predict the rainfall and temperature in the study area. The R2 and NS coefficients obtained in simulating meteorological station data by Miroc5 model with RCP8.5 scenario have values above 0.9, which are good results, and the RMSE coefficient shows that the rainfall and the minimum and maximum temperatures are, in a monthly scale, erroneous by about 2.81, 0.17 and 0.29 mm, in Hamedan station, 4.32, 0.27 and 0.21 in Tuyserkan station and 5.52, 4.42 and 3.82 in Ekbatan, SalehAbad and Maryanaj stations, respectively. In Hamedan station, the rainfall and, the minimum and maximum temperatures are erroneous by 5.3, 0.8 and 0.9%, in Tuyserkan station these values are 5.4, 1.2 and 0.7% and in Ekbatan, SalehAbad and Maryanaj stations they are 8.6, 8.3 and 7.2%, respectively.

Table 6 Summary of Alvand mountain basin model statistics with RCP8.5 and RCP4.5 scenarios
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The average monthly rainfall and, the minimum and maximum temperatures of the five meteorological stations, which simulated by the outputs of the CMIP5 model (Miroc5) with the RCP8.5 scenario in period of 2020–2040, are shown in Fig. 6. Where the rainfall is the lowest in June to September (dry season) and the temperature is, contrarily, at its maximum possible.

Fig. 6
figure 6

Average monthly rainfall and the minimum and maximum temperatures (2020–2040)

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Figure 7 shows the predicted runoff with SWAT for Pole Aliabad, Maryanaj, TaghsimAb and SalehAbad stations under CMIP5 models (GFDL-CM3, EC_EARTH, Hadgem2_ES, Miroc5) and two scenarios (RCP4.5 and RCP8.5). According to the Fig. 7, it can be concluded that the predicted runoff under Miroc5 model is more than runoff under other models in all the stations. But, the lowest predicted runoff in the study area is under GFDL-CM3 model.

Fig. 7
figure 7

Runoff simulated with CMIP5 model for SalehAbad, TaghsimAb, Maryanaj and pole Aliabad stations during 2020 to 2040

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The Z statistical values for Pole Aliabad, TaghsimAb, Maryanaj and SalehAbad stations simulated under RCP4.5 and RCP8.5 scenarios are listed in Table 7 where the runoff from 2020 to 2040 has a positive trend in most stations under different scenarios, but has no significant trend in 90, 95 and 99% probabilities in any of the stations; the highest runoff increase belongs to RCP4.5 and RCP8.5 scenarios in SalehAbad station with the GFDL-CM3 model. In Table 8 that shows the S statistical values of the trend line slope criterion, the highest slope belongs to SalehAbad station (1.46) for the GFDL-CM3 model under RCP4.5 and RCP8.5 scenarios; this slope is positive showing a runoff increase, but only a little.

Table 7 Statistical values of Z for SalehAbad, TaghsimAb, Maryanaj and Pole Aliabad stations
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Table 8 Statistical values of S (trend line slope) for SalehAbad, TaghsimAb, Maryanaj and Pole Aliabad stations
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To check the uncertainty range of the present study’s climate change models on runoffs resulting from the SWAT model, first their outputs were produced in the form of monthly average temperature and rainfall, then their differences were calculated (for each model) using the average of the base period and their variations were plotted as box diagrams and, finally, the box plot resulting from the runoff output of the SWAT model, which is under the temperature and rainfall of climate change models, was drawn. Figure 8 shows the box plot of the temperature and rainfall predicted by Miroc5 model with RCP8.5 scenario, which was the best model for the study area. As shown, rainfall variations are high in wet season and low in dry season (Jun, July and August). The highest variations belong to Ekbatan Station in October; the highest/lowest coefficient of temperature variations relate to the months of winter/summer. In Fig. 9 that shows the box plot of the runoff predicted by SWAT model under the Miroc5 climate change model with the RCP8.5 scenario, an increase in the coefficient of rainfall/temperature variations in wet seasons also increases the coefficient of the variations of the runoff simulated with the SWAT model, but in dry seasons (June, July, Aug. and Sept.), runoff variations are more than the temperature and rainfall variations; most variations belong to the TaghsimAb Station in Dec. and June.

Fig. 8
figure 8

Future temperature and rainfall boxplots

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Fig. 9
figure 9

Future runoff boxplots

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Table 9 shows the percentage of predicted runoff variations in the period of 2020–2040 compared to the period of 2003–2017 under the CIMIP models. As shown, under Miroc5 (RCP8.5) model, the surface runoff in Pole Aliabad, Maryanaj, TaghsimAb and SalehAbad hydrometric stations is, respectively, 6.55, 2.56, 12.69 and 11.65% less in period of 2020–2040 compared to 2003–2017. The largest decrease in runoff in the period of 2020–2040 compared to the period of 2003–2017 is related to the GFDL-CM3 (RCP8.5) model (75.68%). As whole, under all models, the amount of average runoff decreases compared to the past.

Table 9 Percent future runoff variations based on past measurements
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Table 10 shows the runoff variations in all seasons in compared to the past under the models; as shown, the runoff under Miroc5 (RCP8.5) model increases in the basin by 99% and 165% in autumn and summer in compared to the past, respectively, but in the spring, runoff decreases by 67%. The highest runoff reductions found by GFDL-CM3 model under RCP4.5 and RCP8.5 scenarios are, respectively, − 60% and − 69% for winter. For spring, too, the highest reduction is related to the same model under the same scenarios, but for summer, it is related to Hadgem2_ES model with the same scenarios and amount, respectively, to − 79% and − 40%. Among all seasons, the highest runoff reduction, compared to the past, is − 75% for autumn. As whole, on a seasonal scale under all models, the amount of runoff decreases compared to the past, except under the scenario of RCP4.5 in the fall season which is unchanged (0%).

Table 10 Percent runoff variations in all seasons and for all periods and scenarios in relation to the past
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Table 11 shows the runoff variations in all months in compared to the past under the selected models; as shown, the highest average increase of runoff in the basin is by 222% under selected models, in September, but the highest average decrease is 78% in April. Among the models, the GFDL-CM3 model shows the highest reduction of runoff under the RCP8.5 scenario in April (87%) which this reduction is 73% under Miroc5 (RCP8.5) model. Also, between the models, Miroc5 (RCP8.5) shows the highest increase of runoff in the basin, in September equal to 1102%.

Table 11 Percent runoff variations in all months for all periods and scenarios in relation
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Figure 10 shows the SDIs in period of 2003–2017 for Pole Aliabad, Maryanaj, TaghsimAb and SalehAbad stations using the log normal distribution; the average SDI was normal for TaghsimAb and Maryanaj stations in the 2003–2017 period. A severe drought encountered for Pole Aliabad station in the 2008–2015 period and a moderate drought (−1.01) for SalehAbad station in the period of 2003–2017.

Fig. 10
figure 10

SDI series in study stations for the 2003–2017 period

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The SDI predicted for the 2020–2040 period is shown in Fig. 11. Pole Aliabad station face severe drought (−1.84) under the Miroc5 model with scenarios of RCP4.5 and RCP8.5, other models had normal values in this station. At the Maryanaj station, SDI shows normal (−0.06) under Miroc5 (RCP8.5) model and mild drought for other models under RCP4.5 and RCP8.5 scenarios; this station will face extreme drought (−3.88) in 2022 under Miroc5 model with RCP4.5 scenario. As whole, at TaghsimAb and SalehAbad stations, the SDI under all models showed mild drought, But under the GFDL-CM3 model, the SalehAbad station experiences extreme droughts in 2026 (−4.35) and 2021 (−4.28). Also, TaghsimAb station faces extreme droughts in 2025 and 2026 under Miroc5 (RCP8.5) model.

Fig. 11
figure 11

SDI series in study stations for the 2020–2040 period

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Table 12 shows the percentage of SDI variations in period of 2020–2040 compared to 2003–2017 in the basin for under the selected models. As shown, the drought intensity in the Alvand basin will increase under all scenarios (126%). The highest increase of SDI occurs under Miroc5 (RCP8.5) model (180%) and the lowest increase of SDI (77%) occurs under Hadgem2_ES (RCP4.5) model in the basin. In stations of Pole Aliabad, Maryanaj, TaghsimAb, and SalehAbad, the average of highest increase of SDI under the all models is in the months of January (5505%), December (125%), January (201%), and December (100%), respectively.

Table 12 Percent future SDI variations compared to the past
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4 Discussion

In studies related to the effects of the climate change on the environment, CMIP3 to CMIP6 models have had satisfactory results in various researches (Sharafati and Pezeshki 2020; Shadkam et al. 2016; Vaghefi et al. 2019). The present research has used the CMIP5 model to study the effects of the climate change on runoffs and hydrological drought, and, among the selected models and scenarios, Miroc5 model under the RCP8.5 scenario had the best predictions for the Alvand mountainous basin. Comparing the results of CMIP5 (used in this study) with those of CMIP6 (relatively new) have shown that ACCESS-CM2 and Miroc5 models have good rainfall predictability in, respectively, CMIP6 and CMIP5 (Kamruzzaman et al. 2021). Zamani et al. (2021), too, have shown that CMIP5 performs better than CMIP6 in the fall season, but, in general, CMIP6 predicts the rainfall and temperature more accurately. Many global-scale GCM models have been developed to predict the future climate conditions (Hoegh-Guldberg et al. 2019; Piao et al. 2019). Since uncertainty is central in GCMs, and natural variability and resolution can affect them, downscaling is essential to adapt outputs of GCMs and conditions of the desired area (Zhou et al. 2020); among conventional techniques, random downscaling is the one worth mentioning. The Lars-WG model allows the user to generate daily weather data considering the changes in the variables. GCM results under different scenarios showed that Lars-WG predicted the air temperature better than the rainfall, which is consistent with the results of Doulabian et al. (2021). The very practical semi-distributive SWAT model requires future temperature and rainfall to estimate the future river-flow. Analyzing future river-flow characteristics such as the presence of a significant trend/homogeneity or occurrence of hydrological drought conditions is vital to make proper decisions on issues related to the basin assessment/planning systems. The above model has simulated the studied area well, but has been relatively erroneous in simulating the runoff peak, which is consistent with the results of Sharafati and Pezeshki (2020) and Zakizadeh et al. (2021); however, this weakness does not hinder the study of hydrological drought, which is the primary objective of this research. General results of climate change studies on runoffs in the region (under the models and scenarios mentioned in this study) have shown that runoffs will decrease significantly during 2020 to 2040 due to reduced rainfalls and increased temperature. These results do not conform to those of Zakizadeh et al.’s (2021) found in relatively flat Darabad area, Tehran (Iran) that show (under RCP2.6, RCP4.5 and RCP8.5 scenarios with the CanESM2 model) runoffs will increase in the mentioned basin. It seems that the decrease in runoff will be due to reduced snowfalls in the region because the past years’ decreasing snowfall trend approves it; hence, it can be concluded that snowfalls will decrease during 2020 to 2040 causing runoffs to decrease in dry seasons.

5 Conclusion

The current study used the soil and water assessment tool (SWAT) with SUFI2 algorithm to evaluate the past daily and monthly runoffs, predicted the effects of 4 CMIP5 climate models (Hadgem2_ES, EC_EARTH, GFDL-CM3, Miroc5) and two emission scenarios (RCP4.5 and RCP8.5) on 5 meteorological stations (Ekbatan, SalehAbad, Maryanaj, Pole Aliabad, and TaghsimAb in Alvand mountain basin and studied the effects of climate variations on the monthly flow. According to the results, SWAT simulated the daily and monthly runoffs well and was quite capable in the Alvand mountain basin. The results showed that, the best model for the prediction of temperature and rainfall in the region was the Miroc5 model with the RCP8.5 scenario among the climate change models from Cmip5. According to the results found from the mentioned models and scenarios where GFDL-CM3 model with RCP8.5 scenario predicted the least runoff compared to other models, the 2020–2040 future runoffs will decrease (75.68%) compared to the past and the Alvand mountain basin will face such problems as increased temperature, reduced rainfall and, hence, reduced surface runoff. Also, according to the best model (Miroc5 (RCP8.5)), the amount of runoff will decrease by 8.36. The Mann–Kendall Trend Test results show that the 2020–2040 runoffs will be increasing although the trend is not significant. The SDI calculations also show that the drought severity will increase in future compared to the past which, for the best model (Miroc5 (RCP8.5)) this value was 180%. As the population is growing fast and a large part of the agricultural and domestic water consumption in Hamedan is supplied from rivers flowing in the Alvand mountain basin, management plans are quite important in this area and play a key role in providing water resources and solving the future water crises problems.