Introduction

Energy plays a key role in our society, since activities such as housing, transportation, industry, and agriculture depend on it. In addition to the risk on a local scale, energy production from fossil fuels affects environment globally. Co2 emissions contribute to global warming. The solution to this problem seems to be gradual quit using fossil fuels and their replacement with less harmful energies such as renewable energies (Rojey 2009). On the other hand, the rapid growth of demand for electricity and finite amounts of world fossil fuel resources prove the necessity of a greater effort in generating power from renewable energies (Besarati et al. 2013). One of the actions being taken into account across the world to reduce anthropogenic greenhouse gases emission is to replace fossil fuel with lower or zero-emission sources such as solar photovoltaic plants (Cook et al. 2018). As one of the most popular renewable energy sources, solar energy is becoming more popular for many reasons such as increasing environmental pollution resulted from fossil fuels burning, global warming, greenhouse gases emission into the atmosphere and acid rains (Akkas et al. 2017). Solar electricity is rapidly growing. According to the International Energy Agency (IEA), it will grow up to 20–25% by 2050. The IEA has also foreseen that, by 2050, the PV and CSP systems will rise to 6 billion tones (Charabi and Gastli 2011).

Along with the rising in popularity of solar energy, different technologies have been developed. Today, there are two common types of solar technology (converting solar radiation into electricity): concentrated solar power technology (CSP) and solar photovoltaic (PV). Compared to CSP, PV technology is based on the direct conversion of solar radiation into electricity; while CSP is based on converting solar energy into heat using mirrors, heat is then converted into electricity using steam turbines, gas turbines, or stirling engines. Charabi and Gastli (2011) noted that CSP requires more water than PV to cool and clean the mirror. Therefore, for arid countries, PV type is more suitable than CSP. In addition, PV plants are much faster than CSP ones, giving them more flexibility to easily adapt to development of grid system (Khemiri et al. 2018). Solar PV does not emit greenhouse gases or other pollutants, additionally its water consumption is little or zero. Because in hot or arid areas, local air pollution and use of fresh water for cooling of thermal power plants are a serious concern, these advantages of PV are of great importance (Sharma and Singh 2018). In this regard, determining the suitable geographic areas for establishing large‐scale solar power plants is a complex issue; in addition to solar irradiation, technical, economic, environmental, and social aspects should be taken into account. Such considerations need to be made simultaneously. For example, high potential areas may have high biodiversity value too; therefore, they are not suitable for establishment of solar power plants (Rediske et al. 2018).

Many previous studies have been conducted to optimize the site selection for solar power plants using different methods in many regions around the world. Janke (2010) identified suitable areas for wind and solar farms in Colorado. He concluded that areas in northwestern Colorado and east of Denver are suitable for solar farms. Charabi and Gastli (2011) used FLOWA module in order to assess land suitability to install large photovoltaic farms in Oman. Resultant map indicate that a small portion of the Oman show a high suitability. Sun et al. (2013) analyzed geographical and technical potential for exploiting solar energy in suitable areas in Fujian Province. They used land cover and DEM database to extract the geographical constraint factors and divided suitable areas to built-up and non-built-up areas. Lozano et al. (2013) used AHP and TOPSIS methods to identify suitable areas for the installation solar photovoltaic plants in the area of Cartagena in southeast Spain. Tahri et al. (2015) used AHP to weight location, orography, land use, and climate in order to assess existing (NOOR I) and potential sites (NOOR II, III) in southern Morocco. They concluded that 3 factors, namely high potential solar radiation, land surface temperature, and the orientation towards the south are key factors that affects the suitability of an area for photovoltaic farm installation. Farthing et al. (2016) used factors such as land use, land cover, land slope and aspect and solar irradiation to determine locations for the implementation of utility scale photovoltaic in south California. They rank the lands from 0 to 100 and concluded that 4.2% of state land area obtained the midrange value of 70. Chakraborty et al. (2017) classified India into 15 climatic zones based on annual average global horizontal insolation and day-time temperature. They calculated energy output of different photovoltaic in climatic zones. The results achieved indicated the best suitable photovoltaic technology for climatic zones. Uyan (2017) used geographic information system and analytical hierarchy process in order to determine suitable locations for solar power plant in Ayranci region in Karaman, Turkey. He considered five criteria and twenty-one sub-criteria. The generated suitability map was grouped into three categories. Zoghi et al. (2017) investigated solar panels locating using AHP, FUZZY, and WLC methods. They considered environmental, geomorphological, location, climatic, and constraints criteria and concluded that region under consideration had high potential in order to install solar panels. Akkas et al. (2017) used the multi-criteria decision making methods (AHP, ELECTRE, TOPSIS, and VIKOR) to site selection for a solar power plant. They selected five cities from the Central Anatolian Region of Turkey for the study. Karaman has been identified as the most suitable city for solar power plant installation for all of the methods. Majumdar and Pasqualetti (2019) assessed land suitability for solar PV in Arizona. They considered topography, location, solar resource, and public opinion and concluded that less than 2% has excellent suitability for solar PV development in Arizaona. Agyekumet al. (2021) used AHP and density-based clustering for photovoltaic power plant site selection in Ghana. They identified 3 cluster and ranked them as cluster 1, 3, and 2. Khan et al. (2023) analyzed ten factors to determine suitable sites for solar PV power plants. Weights of factors were assigned using full consistency method. A suitability map showed that 2.02% of the country’s total area is appropriate for construction of solar PV power plants. Grazia and Tina (2024) identified suitable sites for floating photovoltaic system. Two multi-criteria decision-making approaches (AHP and TOPSIS) were used as the analysis method. Among seven studied watersheds, the San Giovanni dam was identified as the best location for the installation of floating photovoltaic plants in the study area. Rane et al. (2024) conducted a site selection study for solar photovoltaic power plants in Nashik, India. Optimal site for installation of PV power plants were determined using GIS-based multi-influencing technique. The results of a sensitivity analysis showed that solar radiation, relative humidity, and elevation are the most sensitive factors.

The catastrophe theory has been employed in different fields. Kheirizadeh Arouq et al. (2020) assessed vulnerability of Tabriz to earthquake based on this approach. Ahmed et al. (2015) and Sadeghfam et al. (2016) used catastrophe theory for assessing ground water potential zones. This approach was applied in other fields such as land ecological security (Su et al. 2011); vulnerability to floods (You and Zhang 2015); assessment of flood hazard risk (Li 2011); landslide evolution (Tao et al. 2013); and rural infomatization level (Zhang et al. 2011).

In the present study, the optimal locations for the installing of solar power plants in East Azerbaijan province located in Northwest Iran are evaluated by using environmental and human factors. A set of factors such as high population density, several large cities—especially the metropolis of Tabriz—and hundreds of large and small settlements, industrial hub in the northwest of the country and numerous factories and industrial towns, the center of agriculture and the need to modernize the agricultural sector of the province and of course to energy resources (especially electricity), the environmental diversity, the need to reduce various environmental pollution from fossil fuel consumption (Tabriz thermal power plant can be pointed out which in recent years has been one of the most important sources of air pollution in the Tabriz), and so on necessitates the use of solar energy in the province. Lack of attention to the site selection of photovoltaic power plants may cause the inefficiency and waste of economic resources in the province. In the present study, environmental variables were taken into account in order to evaluate solar energy potential and socio-economic variables to consider the economic efficiency of solar power plants. Due to the spatial nature of the location of solar power plants, all the factors influencing the location of these power plants were integrated in GIS environment.

The current study focuses on the catastrophe theory to identify suitable locations for solar power plant in East Azerbaijan province. East Azerbaijan province is one of the industrial centers in Iran, where a large number of industries and factories are located. It is also one of the densely populated regions of Iran, which, in addition to the metropolis of Tabriz, has several large cities such as Maragheh, Marand, and Ahar. The province has seen significant industrial growth in recent years, leading to a surge in energy demand. However, East Azerbaijan faces challenges due to its limited energy resources and distance from Iran’s main oil and gas reserves in the south, resulting in higher energy transmission costs. On the other hand, the study area has a semi-arid climate and has water scarcity issues. Recent droughts and poor water management have led to the drying up of Lake Urmia in the west of the province. As a result, there is a pressing need to shift towards renewable energy sources to meet the growing energy demands sustainably. So, the objectives of this study are twofold: (1) to apply functions of catastrophe theory to eliminate or reduce uncertainties in the decision-making process; (2) to evaluate solar energy potential in East Azerbaijan province; (3) to explore the suitable areas for the installation of solar panels in East Azerbaijan province.

Materials and methods

Study area

In the current research, the optimal site selection for solar photovoltaic (PV) power plants in East Azerbaijan province has been discussed. With a population of nearly four million people, it is one of the most densely populated provinces located in the northwest of Iran. It lies between 36° 45′ to 39° 26′ longitude and 45° 5′ to 48° 22′ latitude (Fig. 1). With a total area about 45491 km2, this area occupies 2.8% of whole country. The province has 21 counties, 48 districts, and 70 cities. About 73% of the population of the region are urban dwellers. Tabriz, as the most populated city and the capital of East Azerbaijan province, has a population of 1,584,855, which is about 40.54% of the total of the province.

Fig. 1
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Location map of East Azerbaijan in Iran

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The study area consists of structural plains and mountain around them. Most of the mountain ranges of the region are extended in the west–east. In terms of topography, the study area is characterized by seven mountain units (Qaradagh in the north, Ghoshadagh in the northeast, Sabalan volcanic massif in the east, Bozgosh in the southeast, Mishodagh in the northwest (north of Lake Urmia), Sahand volcanic mass in the west, and Takht Soleiman in the south) with valleys and plains between them. Many plains have been formed among the mentioned mountain units, including Tabriz, Maragheh, Ahar, Sarab, and Mianeh Plains. The distance area between the plains and the mountains provides suitable conditions for the construction of solar photovoltaic (PV) power plants in terms of receiving solar energy. In the formation of different climates in the province, the influence of topography can be clearly seen. With the increase in altitude, the semi-arid climate of the plains, hills, and low mountains of the province becomes the Mediterranean climate of the middle levels of the high mountains. Towards the top of the mountains, the Mediterranean climate becomes a semi-humid and humid climate, respectively. The average annual precipitation is 250 to 300 mm. According to this climate type, the vegetation of East Azerbaijan province is mainly in the form of steppe. The forest is limited only to parts of the Qaradagh mountain range in the north of the province with a more humid climate. The dominance of semi-arid climate in a wide area of the province provides relatively favorable conditions for the construction of solar photovoltaic (PV) power plants.

Methods

In GIS modeling, the relative importance of one criterion over other is determined using weighting. Several methods for weighting are mainly divided into two groups, objective and subjective. In subjective weighting methods, weights are assigned according to the information, knowledge, and preference of decision makers. On the other hand, mathematical models are used in the objective weighting method. In the present study, in order to calculate the relative importance and overlaying thematic maps affecting the optimal location of solar photovoltaic power plants in East Azerbaijan province, catastrophe theory is used to avoid the subjectivism. Catastrophe theory evaluation method does not take into account the preference of decision makers. Rather, it calculates the importance of one criterion over other by its internal mechanism and thus greatly reduces subjectivism.

Catastrophe theory which originates from the branch of mathematical topology, was first proposed by a French scientist named Rene Thom in the 1960s. The main goal of this theory is to handle the phenomenon of discontinuity. The catastrophe method, which is based on catastrophe theory, uses hierarchy, fuzzy evaluation, and utility function to obtain fuzzy catastrophic membership functions. The dependence of state variables on control variables is determined by catastrophe fuzzy membership functions, instead of weights assigned by users. However, in catastrophe theory, the effects of different control variables on the state variables are not the same.

As shown in Table 1, there are seven catastrophe models namely, fold catastrophe, cusp catastrophe, dovetail catastrophe, butterfly catastrophe, swallowtail catastrophe, hyperbolic umbilical catastrophe, and parabola umbilical catastrophe (Ahmed et al. 2015).

Table 1 Seven types of catastrophe models (Ahmed et al. 2015; Xiao-jun et al. 2012)
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The process consists of the following steps: (i) creation of an indicator system; (ii) standardization of data; (iii) normalization for catastrophe theory; and (iv) integration of thematic maps. The steps are discussed in details as follows:

Creation of an indicator system

There are many criteria that affect the solar photovoltaic power plants site selection, including sunshine hours, slope, aspect, distance to residential areas, and so on. Selection of indicators mainly depends on the purpose of the study and the data availability. Different criteria have been used by researchers to assess suitable lands for solar power plants installation. Farthing et al. (2016) considered factors such as land use, the type of land cover, slope, aspect, and solar radiation. Uyan (2017) used buffer of residential areas, roads, rivers and lakes and of natural preserve areas as constraints. Al Garni and Awashti (2018) provided a list of criteria and sub criteria used by different researchers. They categorized the criteria into seven groups: environmental, location, economic, climatic, orography, social, and risk. Also, they presented the list of restrictions used in solar energy studies. Low solar radiation, protected land, roads and railroad network, higher slope areas, dams and the land aspect are some restrictions used in solar power site selection studies. They concluded that protected land, cultivated, and high landscape areas along with watercourses and streams are the most excluded areas. In solar site suitability studies, criteria such as urban areas, protected land, major road networks and higher slope lands (> 5°) have been considered constraint factors (Al Garni and Awashti 2017). Rediske et al. (2018) verified that solar irradiation, substation distance, slope, distance of roads, distance from urban areas, and land use are key factors for site selection of solar photovoltaic power plants. Based on the review of literature and on the available data, a set of 17 evaluation criteria were organized in four point of view: climatic, geomorphological, environmental, and access-economic.

In the present study, the optimal location of solar photovoltaic power plants was considered the main system, which can be divided into four subsystems: climatic, geomorphological, accessibility-economic, and environmental. Each subsystem has its own characteristics to show the potential of solar power plant construction. The components of the system and subsystem are strongly related to each other and determine the potential of a site for the construction of solar photovoltaic power plants. Based on the research literature as well as the available data for the study area, the used variables to locate solar photovoltaic power plants can be classified as follows:

  • Climatic factors: These factors have a great effect on the amount of solar radiation received and consequently on the spatial potential of solar photovoltaic power plants. Solar radiation, average annual temperature, sunshine hours, and relative humidity are the most important criteria of this subset.

  • Geomorphological factors: These factors are of great importance due to their effect on the amount of received radiation, access and providing a suitable land for the establishment of photovoltaic power plants. Elevation, slope, aspect, distance to faults, landslide prone areas, and distance to rivers are included in this group.

  • Environmental factors: These factors are very important in terms of environmental protection and avoiding or minimizing the adverse environmental effects of the construction of solar photovoltaic power plants. Land use, vegetation, and distance to protected areas are among the most important variables in the set of environmental factors.

  • Access-economic factors: Population density, distance to transmission lines, cities, main roads and to the communication network are considered a subset of these factors.

In conducting our research, we utilized a variety of data sources to perform our model for site selection of photovoltaic power plants. Spatial distribution of elevation, solar radiation, slope, and aspect was derived from DEM data of ASTER image with 28-m spatial resolution. Geological map at 1:100,000 scale of geological survey of Iran was used in order to derive distribution of faults. Climatic data was sourced from synoptic stations in East Azerbaijan province, while Landsat 8 satellite images were used to create NDVI maps. Additionally, information on land use, rivers, and landslide risk was provided by the Natural Resources Organization of East Azerbaijan province. The protected areas of the province were prepared through maps provided by Iran’s environment department. Demographic data came from the Iran Statistics Center census, and power transmission line locations were sourced from East Azerbaijan Regional Electric Company.

Standardization of data

In multi-criteria decision making methods, different indicators have different units of measurement. It is not possible to use heterogeneous units in data analysis for this model. Therefore, data standardization is essential. The standardization process makes the data dimensionless. In the present study, the following equations were used to standardize the thematic layers affecting the optimal location of solar photovoltaic power plants.

Equations (1) and (2) are used for the standardization of “larger the better” and “smaller the better” indices, respectively:

$${{x}{\prime}}_{i}=\frac{{x}_{i}-{x}_{i}{}_{({\text{min}})}}{{x}_{i({\text{max}})}-{x}_{i({\text{min}})}}$$
(1)
$${{x}{\prime}}_{i}=1-\frac{{x}_{i}-{x}_{i}{}_{({\text{min}})}}{{x}_{i({\text{max}})}-{x}_{i({\text{min}})}}$$
(2)

where i is the index of attribute, xi is the original value of i, and xi(max) and xi(min) are maximum and minimum values.

Normalization for catastrophe theory

Generally, data are normalized after the system decomposition into several subsystems. Normalization equations are the basis for catastrophic theory. Catastrophic progression of each control variable can be calculated from the initial fuzzy subordinate according to normalization formulas (Table 2). During the calculation process, two principles are used: the complementary and the non-complementary. The non-complementary principle means that the control variables of a system such as a, b, c, and d cannot be replaced with each other (compensate, neutralize, or balance each other). Therefore, while finding the value for the state variable x using the normalization formulas, the smallest values of the state variable corresponding to the control variables, i.e., \(x={\text{min}}\left\{{x}_{a},{x}_{b},{x}_{c},{x}_{d}\right\}\) are selected as the value of the state variable of the whole system. On the other hand, the complementary principle implies that the control variables complement each other so that they tend to reach the mean value, i.e., \(x=\left\{{x}_{a},{x}_{b},{x}_{c},{x}_{d}\right\}/4\) (Ahmed et al. 2015). In the present study, the complementary principle was used to calculate the catastrophic progression of each control variable.

Table 2 Normalization formulas for catastrophe theory (Ahmed et al. 2015)
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Integration of thematic maps

In the last step, all thematic maps were integrated within GIS using the coefficients obtained from catastrophe theory functions. Then the land suitability of East Azarbaijan province was evaluated for the construction of solar photovoltaic power plants. The research process flowchart is given in Fig. 2.

Fig. 2
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Overall methodological flowchart of site selection for PV power plants

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Results and discussions

Indicator systems

Climatic factors

The spatial distribution of climatic variables is presented on Fig. 3. The average solar radiation in the province is about 636860 kWh/m2. While the minimum and maximum values of solar radiation observed are 41694 kWh/m2 and 952011 kWh/m2. East Azerbaijan province has a high potential and spatial variability in solar radiation. In comparison, the southern half of the province receives more solar radiation due to its low latitude. This is especially obvious on the southern slopes of the Sahand volcanic massif and the Bozqush mountain range. The lowest amount is seen in the northern part of the province. These zones correspond to the northern slopes of the Qaradag Mountains. High latitude and shading are the most important factors affecting the reduction of radiation received in these areas. The average annual air temperature in the province varies from 8.9° C in Sarab to 15.3° C in Ajabshir. Temperate zones are highly desirable in the location of photovoltaic power plants. The average annual sunshine hours in East Azerbaijan province is 2932 h, which is a large value. The average monthly value is 241.7 h with a standard deviation of 8.3. The hill slope and plains in east of Lake Urmia have the greatest amount of sunshine; thus, they are considered optimal locations for establishment of solar photovoltaic power plants. Finally, the relative humidity increases from west to east in the province. Therefore, in the western part of the province, due to the low relative humidity, the panels of solar photovoltaic power plants will have high efficiency.

Fig. 3
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Spatial distribution of factors affecting optimal site selection for solar power plants in East Azerbaijan province

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Geomorphological factors

In the present study, elevation, slope, aspect, distance to the fault, rivers and water resources and to landslide hazard areas (lands that are subject to landslide hazard) were organized in subsets of geomorphological factors. The average elevation of East Azerbaijan province is 1672.5 m with a range of 4268 m. Considering the decrease in energy received at low elevation and difficult accessibility at high elevation, the average elevation levels, i.e., elevation classes 1396 to 1578, 1579 to 1740, and 1741 to 1902 can be considered suitable elevation levels for the construction of solar photovoltaic power plants. As the slope increases, the land suitability for the construction of solar photovoltaic power plants decreases. In the present study, slopes of less than 5% were considered ideal slopes, which cover 21.6% of the total area. The southern, southwestern, and southeastern aspects are very important in terms of solar radiation received. In the province of East Azerbaijan, the southern, southwestern, and southeastern aspects are about 12.5%, 12.1%, and 12% respectively. The distance map to fault was prepared and used in the site selection of solar photovoltaic power plants. In this regard, a 3 km buffer zone for faults in the region can reduce the dangers of fault movement. In the province, where there are marls, conglomerates, and deeply weathered sediments, the probability of landslides is high. This is a key factor in locating solar photovoltaic power plants in East Azerbaijan province and the construction of such plants in these areas is generally not preferred. Finally, consideration of flood zones shows that they occur more in floodplains adjacent to rivers. Because flood risk zoning maps are not available for the province, distance to rivers and water resources was used as an alternative.

Environmental factors

In the present study, land use, vegetation, and protected areas were organized in the set of environmental factors. Very suitable land uses for the construction of solar photovoltaic power plants include rain-fed lands, low-density pastures, and barren lands, which cover 28. 9 and 0.3% of the province area, respectively. The semi-dense pasturelands also have a relatively high suitability for the construction of such power plants which represents about 29.5% of its total surface. The Normalized difference vegetation index (NDVI) index was used to show the impact of vegetation cover in the location of photovoltaic power plants. NDVI values between 0 and 0.09 indicate barren lands or little vegetation cover. This class occupies 27.5% of the area of East Azerbaijan province. NDVI values between 0.1 and 0.14 indicate pasturelands with poor vegetation and rain-fed lands. This class covers about 42% of the province. Mentioned classes are considered the most desirable areas for the establishment of solar photovoltaic power plants taking into account vegetation. This class includes considerable parts of the plains, downhills, and middle slopes of the mountains of the province. In the case of protected area, with the exception of Lake Urmia National Park, most of these areas correspond to parts of the mountains of the province. Due to the restrictive laws in these areas, the establishment of photovoltaic power plants in these areas is not preferred.

Access-economic factors

Population density, proximity to urban centers, roads and to the main transmission lines were organized in the framework of access-economic factors. Due to the high costs associated with construction of power lines, distance to transmission lines is one of the important criteria which should be considered in site selection for solar power plants (Noorollahi et al. 2016). To contribute the proximity to power lines, 230 and 400 kW transmission lines were used in the province and the distance map to them was provided (Fig. 2). From this point of view, the central parts of the province, especially due to Tabriz metropolis and satellite cities and towns, are in much better condition.

In terms of population density, a large part of the population of the study area is concentrated in the western half of the province. Meanwhile, the central part of Tabriz city with a population density of 852 people per km2 is the most densely populated area in East Azerbaijan province, which is due to location of the metropolis of Tabriz. Generally, the main concentration of the population corresponds to the eastern plains of Lake Urmia. It should be noted that the proximity of solar photovoltaic power plants to cities is not preferred. In fact, the presence of various sources of pollution and dust in and around cities can have a negative impact on solar energy reception by solar panels. It is likely that these power plants locate in the path of physical development of cities, which is not desirable. Thus, in the present study, an area was considered buffer of cities. Finally, proximity to the major transportation network was used as one of the sub-criteria of access-economic factors in the location process of solar photovoltaic power plants.

Normalization of thematic maps

As explained above, indicator systems and related variables do not have the same unit (e.g., the slope expressed as a percentage, distances as meters, etc.), and thus, they cannot be used in the process of locating solar photovoltaic power plants. It is then necessary to match the units for each thematic map. Generally, in implementing a catastrophe theory-based model, data standardization has several major goals. First, the units of all thematic maps are matched. Accordingly, this makes thematic maps dimensionless and the values are in the range between 0 and 1. Second, each thematic map is revaluated according to the purpose of the research. For example, there is an inverse relationship between the optimal sites for the construction of solar photovoltaic power plants and the slope; thus, as the slope increases, the suitability of the lands for the construction of such power plants decreases. As a result, it is necessary to revalue or change the pixel values of the slope layer by using special equations. Finally, each standardized thematic map is used continuously (rather than discretely) in the process of overlaying the layers in the context of the geographic information system (GIS). This largely eliminates the uncertainties associated with reclassifying layers.

Computation of fuzzy membership function and multi-criteria decision-making based on the catastrophe theory

Thematic maps were normalized and according to the complementary principle, the relative weight of each variable was calculated. In complementary principle, the control variables complement each other and tend to mean value. In the present study, the following functions were used to normalize and calculate the relative weights of each criteria and finally to integrate the indicator systems.

The thematic layers of solar radiation, sunshine hours, elevation, slope, land use, population density, and distance to the city have five control parameters and as a result were normalized using the Wigwam equation. This is because of the large spatial variability of these variables in East Azerbaijan province. Determining the type of catastrophe fuzzy function highly depends on the spatial distribution of variables and with increasing spatial variability, the type of function tends to the butterfly and wigwam. The thematic layers of relative humidity, temperature, aspect, vegetation cover, distance to the road and to transmission lines have four control parameters and meet the butterfly. The mentioned variables have lower spatial variability than the above-mentioned variables. Distance to fault and landslide hazard prone areas have three control parameters and were normalized by applying the swallowtail. These variables have a more limited spatial distribution in East Azerbaijan province. Finally, the distance to the river and to the protected areas, have two control parameters and meet the swallowtail function. These two variables have the lowest spatial variability compared to other variables used in site selection of solar photovoltaic power plants.

The significant values related to the application of catastrophe theory for the optimal location of solar photovoltaic power plants in East Azerbaijan province are gathered in Table 3. Relative weights of the variables were assigned using the complementary principle and can be summarized as follows:

Table 3 Details of catastrophe weighting method for integrating indicator systems affecting site selection for installation of solar power plants East Azerbaijan
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According to complementary principle, slope, distance to city, solar radiation, and distance to power lines are of the highest importance in optimal location of photovoltaic plants. Based on the complementary principle, the mentioned variables had a weight of more than 0.7. It is important to note that the user does not play a role in determining the relative weight of the variables and they were calculated based on the internal mechanism of the catastrophe system. In fact, this is the most important advantage of the model which minimizes the uncertainties associated with the judgments of experts and specialists. Next comes elevation, distance to the road, vegetation cover, sunshine hours, and land use. The catastrophe system assigns relative weights of 0.683 to 0.696 to these variables. Relative humidity, aspect, and average annual temperature with relative weights of 0.6567, 0.6492, and 0.6429, respectively, are of a moderate importance in the process of optimal location of solar photovoltaic power plants in the East Azerbaijan province. These variables are part of geomorphological and climatic subsystems. One of the reasons for the decrease in the importance of these variables compared to the above-mentioned variables is their uniform spatial distribution in the province.

Relative weights of landslide hazard, distance to fault, river, protected areas, and population density were assigned less than 0.6, and as a result, they are less important in locating solar photovoltaic power plants. One of the most important reasons for the less importance of these variables is their small spatial variability in the province.

Integration of thematic maps to create suitability map for installing solar photovoltaic power plants

In the previous stages of this research, the spatial distribution of each variables affecting the optimal location of solar photovoltaic power plants in East Azerbaijan province was evaluated. Due to the mismatch of the thematic maps units, the layers were standardized. The thematic maps were also normalized using catastrophe theory functions and the weight or impact factor of each layer was calculated. At this stage, the thematic maps affecting the optimal location of solar photovoltaic power plants were integrated according to the weights obtained from the catastrophe theory in the context of GIS.

$$\mathbf{P}\mathbf{V}\mathbf{S}=\sum\nolimits_{{\varvec{i}}=1}^{17}{\varvec{w}}{\varvec{i}}\times {\mathbf{L}\mathbf{a}\mathbf{y}\mathbf{e}\mathbf{r}}_{\mathbf{i}}$$

Thus, by integrating the standardized thematic maps by using the weights obtained from the catastrophe theory, the land suitability map of East Azerbaijan province for the construction of solar photovoltaic power plants was delineated. The suitability map was further classified into five zones viz., “very high suitable,” “high suitable,” “moderate suitable,” “unsuitable,” and “low suitable” (Fig. 4). Figure 5 displays the percentage of area in different land suitability classes for installation of solar power plants, East Azerbaijan province.

Fig. 4
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Suitability map for installing PV systems in east Azerbaijan province

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Fig. 5
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Percentage of each suitability class for construction of PV in East Azerbaijan

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From Fig. 4, it can be noticed that a small portion of the region under consideration (2.1%) and 9.7% exhibit very high and high suitability, respectively. It is also necessary to mention that a considerable part of these zones are distributed only in very limited areas across the province, where in terms of the extent, are not suitable for the construction of the power plant. In fact, the aim of the present study is to locate large-scale solar photovoltaic power plants connected to the national electricity grid, which require large areas of land. Also, in most cases, high suitable lands are distributed within or adjacent to a very high suitability class, which is considered an advantage. The study reveals that about 24.9% of the study area is covered under moderate suitability for the construction of solar photovoltaic power plants which are mainly distributed in the southern half and western parts the northern half of the province. The low suitable and unsuitable lands are observed in 44.2% and 19.1% respectively. These classes are mainly distributed in the northern and eastern half of the province. Geographical isolation, low solar radiation, low sunshine, high relative humidity, high degree of roughness, valuable plant ecosystems, and low population density can be the most important environmental-human reasons. It can be noticed that towards northeast, the land suitability for the construction of solar photovoltaic power plants in the province of East Azerbaijan decreases. A considerable part of the Khodaafarin, Kalibar, Horand, Varzeqan, Ahar, Heris, Sarab, and Jolfa counties in the northern half of the province are located in a low suitable orunsuitable class. Thus, in terms of various environmental (geomorphological, climatic, and environmental) and human aspects (economic and accessibility factors), they are not considered ideal sites. It should be noted that the identification of unsuitable zones for the construction of solar photovoltaic power plants is as important as that of suitable zones. In fact, it is a key factor in avoiding the loss of capital.

Taking into account the area of high and very high proportional classes for the construction of photovoltaic power plants, five zones are highly desirable. These zones, specified using the symbol of the solar panels, located in the southwest and northwest of the province (Fig. 4). The aforementioned zones are desirable for many factors. In terms of climatic factors, the zones identified in the southwest of the province (Malekan and Bonab) are consistent with the peaks of the volcanic mass of Sahand and Gara Goshone which receive solar radiation at a higher intensity. The amount of solar radiation in these zones varies from 584314 to 694980 kW/m2. The amount of radiation received in the northwest of the province (Shabestar and Tabriz) varies from 641432 to 694980 kW/m2 which located in high radiation class. These sites are consistent with the southern slopes of Mishoo and Morodagh. Average sunshine hours in Malekan and Bonab varies from 247 to 256 which is a high value. Shabestar with more than 255 monthly sunshine hours has the highest amount of sunshine among identified sites. Tabriz also receives an average of 239 to 247 h, which is small compared to other identified sites. The annual relative humidity in all identified sites is less than 51%, which is desirable for the efficiency of photovoltaic plants. Also, the average annual temperature of these zones varies from 8 to 11°C, which is relatively favorable. In terms of geomorphological—geological factors, the identified sites for the construction of solar photovoltaic plants have desirable to relatively good conditions. The slope of these zones varies from 0 to 5%. However, parts of Tabriz and Shabestar have a slope between 5 and 10%, which avoids land preparation operations. Due to many desirable environmental aspects of these zones, the costs associated with land preparation can be ignored. The aspect is also mainly southern and western, which improves the amount of solar radiation. The southwest of East Azerbaijan province is one of the most stable areas in terms of geomorphological and geological conditions. However, Shabestar and Tabriz are adjacent to the large Tabriz fault and its various splits, including the faults of the southern slopes of Mishoodagh, so the buffer of these faults should be considered. In the mentioned sites, structural measures are also necessary to control and inhibit the floods. In terms of environmental factors, the major land use in identified zones includes barren lands or rangelands with poor vegetation. Also, these zones are not close to protected areas and do not have various rich animal species. Finally, in terms of economic and access factors, the zones identified by the Catastrophe system in both sites have ideal conditions. In this regard, proximity to the main roads of the province, access to the main power lines, proximity to the largest population centers and to the industrial poles in the province can be referred.

Conclusion

In the present study, 17 environmental-human variables were considered for the optimal location of solar photovoltaic power plants in East Azarbaijan province, located in northwestern Iran which is organized in four points of view: climatic, geomorphological, environmental, and access-economic. The considered variables were integrated in the context of the GIS using catastrophe theory functions. Mathematical basis, extracting the relative importance of criteria based on the internal mechanism of the Catastrophe system, reducing uncertainties in the decision-making process, reproducibility of results, applicability in different geographical conditions, ability to combine different types of data with different scales and sources whithin the GIS can be considered the most important advantages of the GIS-catastrophe approach.

The results show that slope, distance to the city, solar radiation, and distance to power lines are the most important variables affecting location of solar photovoltaic power plants in the province of East Azerbaijan. Conversely, distance to the river, protected areas, and population density have the least impact. Generally, most of the variables that have little spatial variability and perform in a local scale, have gained lower weight in the catastrophe system. Finally, according to the coefficients obtained from the catastrophe theory, the 17 standardized variables were integrated in the context of GIS, and thus, the suitability of the province’s lands for the construction of solar photovoltaic power plants was obtained. Accordingly, East Azerbaijan province was classified into five classes. Most of the northern and eastern parts of the province were in low and unsuitable proportion class (63% of the total area of the province). In fact, the Catastrophe system in these areas did not identify suitable sites for the construction of solar photovoltaic power plants. This is due to the unfavorable areas in terms of many natural-human variables that can be attributed to low radiation, low sunshine, high relative humidity, high degree of roughness, limited flat lands, low population density, poor access to roads and power lines, and the existence of environmentally protected areas. About 25% of the province’s area was in the moderately suitable class, which mainly includes the central and southern parts of the province. These zones have suitable conditions for establishment of solar photovoltaic power plants in terms of some defined variables and unsuitable conditions for a number of others. In general, these zones do not have ideal conditions for the construction of solar power plants and are not considered priorities. According to the final land suitability map for the construction of solar photovoltaic power plants, about 2% of the land in East Azerbaijan province is in a very high suitable and about 10% in a high suitable class. These zones are located in the western part of the province. In these zones, five optimal sites for the construction of solar photovoltaic power plants were identified, which were named as Malekan, Bonab, Ajabshir, Shabestar, and Tabriz sites according to their location. In these sites, in terms of many environmental-human variables, ideal conditions are established for the construction of solar photovoltaic power plants, such as adequate reception of solar energy, high sunshine hours, low relative humidity, suitable slope, poor vegetation, distance to protected areas, proximity to the population centers of the province, excellent access to roads and main transmission lines, and in the case of Malekan, Bonab, and Ajabshir sites, relative stability of geological-geomorphic conditions can be mentioned. Thus, the construction of solar photovoltaic power plants at identified sites—especially southwestern sites—can lead to favorable results both in terms of environmental and socio-economic conditions.

In recent years, numerous studies conducted on the locating of solar power plants have mainly applied GIS-based multi-criteria decision models (MCDM). Georgiou and Skarlatos (2016), Uyan (2017), Kocabaldır and Yücel (2020), and Wang et al. (2020) applied multi-criteria decision models—with emphasis on the analytic hierarchy process (AHP) model and GIS tool—to identify areas that are suitable for solar power plants. The results of these studies indicated the high efficiency of multi-criteria decision models in combination with GIS in site identification for solar power plants. Assessing the ideal locating conditions in a large area, considering multiple variables and their integrated analysis, reducing the time and costs associated with project implementation can be considered the advantages of these approaches. The main problems regarding the use of multi-criteria decision making models—such as the AHP—are subjectivism and the uncertainty of expert judgments in the process of weighting and integration of thematic layers which has led to criticism of such models. In the present study, the uncertainties related to the decision-making process were largely reduced by applying the functions of catastrophe theory. Also, compared to many studies, a large number of variables were used in the process of locating solar power plants.

Our results indicate the high performance of the catastrophe theory in the framework of the GIS for the optimal location of solar photovoltaic power plants. To ensure the accuracy of our model, we initially conducted field studies. According to the field studies, we concluded that the proposed sites have ideal conditions for the establishment of solar power plants, which are also mentioned in the findings and conclusions. In addition, a project by the regional electricity company of East Azerbaijan province (2015) has been conducted for the site selection of photovoltaic power plants in the province, which also includes field studies. The results of this research showed a favorable compliance with the mentioned project. Tabriz solar power plant (constructed in 2015) also corresponds to one of the sites proposed in the current research. It can even be stated that the model based on the catastrophe theory has a lot of strictness, and as a result, it is able to identify the most favorable points for specific purposes. The advantages of the approach used are as follows:

  1. 1.

    It has a mathematical basis and helps to quantify spatial-geographical criteria and objectifies the application of the model in geography.

  2. 2.

    The weighting method in the Catastrophe model is based on the internal performance of the catastrophe system, thus minimizing subjectivism and the uncertainties.

  3. 3.

    It has a high ability to integrate a variety of quantitative and qualitative variables and data types from different sources for a specific purpose. The results of catastrophe theory have reproducibility, which is considered one of the most important advantages of the model. While subjectivity and low reproducibility are one of the most important disadvantages of most multi-criteria decision making methods. The catastrophe theory can be well integrated into GIS and used to solve spatial problems. Finally, the approach used in the present study can objectify the practical aspects of geography and help to make this science more useful.