In order to map the distribution of CO₂ greenhouse gas emissions in the household sector, the annual amount of carbon dioxide emissions was calculated based on the type of fuel consumed in the entire city’s household sector using statistical data for Isfahan city in 2020 and the CO₂ emission calculation method Eq. (1). Then, the results of the annual emission rate of this gas were divided by the total area of all buildings in the city (note that in calculating the area of buildings in the domestic sector, the total area of floors was taken into account). The obtained value represents the amount of carbon dioxide emissions per square meter of fixed sources in the household sector. Finally, to calculate the amount of emissions for each of the buildings in the city, the obtained number (the amount of CO₂ released per square meter) was multiplied by the total area of each building. In this way, the distribution map of carbon dioxide greenhouse gas emissions based on the household sector in the city was calculated (Eq. (2), Table 3).

At this stage, data on the amount of fossil fuel consumption in the commercial-public sector was collected for mapping the distribution of emissions in this sector. Then, based on Eq. (1), the annual amount of CO₂ emissions were calculated. In the next step, the total annual emissions of this gas were divided by the total area of commercial-public areas. The resulting value indicates the amount of CO₂ emissions per square meter in commercial-public areas. This value was multiplied by the area of each building in this sector, and the product shows the distribution map of this gas emission in the commercial-public sector (Eq. (3), Table 3).

Due to the lack of statistical data on the amount of energy consumed by each industry, the mapping stages of CO₂ gas distribution in the industrial sector were calculated similarly to the residential and commercial-public sectors (Eq. (4), Table 3).

Based on the annual consumption of fossil fuels, the amount of CO₂ emissions were calculated for the two power plants located in the study area, and this value was considered for the spatial range of the power plants.

In this step, urban streets were classified into two tiers of main streets (level 1 and level 2 arteries, ramps, collectors, urban expressways, city freeways, suburban expressways, and suburban freeways) and sub-streets. Then, using high-resolution satellite images, the number of vehicles on each of the two tiers of roads (main and sub-streets) was calculated [37]. For this purpose, the time series of Google Earth images were used. Then, the number of vehicles on each class of the road per kilometre was calculated using Eq. (5) (Table 2) [38]. The calculated number of vehicles for each of the two road classes was taken as the weight of that tier of roads in carbon dioxide emissions. Next, to prepare a map of the spatial distribution of CO₂ emissions in each of the two tiers of roads (i.e., main and sub-streets), the weight calculated was multiplied by the total amount of annual CO₂ emissions from the use of fossil fuels in the road transport sector (excluding fuel consumption in the bus transport network). As a result of these steps, the amount of CO₂ resulting from the use of fossil fuels in the road transport system was separated and calculated into two parts: the amount of CO₂ emitted from main streets and sub-streets (the results of this step have been converted into mathematical Eqs. (6) and (7) and are presented in Table 2).

Then, considering that each of the first floor streets (i.e., main streets) differs in terms of transportation traffic, the amount of CO₂ emitted on each of them is also different. Therefore, to calculate the amount of CO₂ emissions per kilometer on each of the main streets (level 1 arterial roads, level 2 arterial roads, ramps, collectors, urban expressways, urban highways, suburban expressways, and suburban highways), the hourly traffic volume must be calculated. To this end, in this study, the results of comprehensive transportation studies in Isfahan in 2019, which had calculated the traffic volume on each of the roads, were used. Finally, the amount of emitted carbon dioxide in each section of the main road types was obtained using Eq. (8) (Table 2). On the other hand, since the amount of transportation traffic in secondary streets depends on the population density in the neighborhoods, the population ratio in the neighborhoods was used as a weight variable to calculate the distribution map of carbon dioxide emissions in the secondary streets in each of the neighborhoods. In this way, the map of CO₂ distribution emitted in secondary streets in neighborhoods was calculated using Eq. (10) (Table 2). Also, in order to calculate the annual CO₂ emissions resulting from the consumption of fossil fuels in Bus Routes, in the first stage, the bus routes map of Isfahan city was prepared. Then, the amount of annual carbon dioxide emissions from fossil fuels in this sector was calculated using Eq. (1). In the final stage, the spatial distribution map of CO₂ emissions in bus lines was prepared using Eq. (12) (Table 2).

In this step, a map of the railway transport lines within the city of Isfahan was prepared. Then, the average fuel consumption per kilometer of the railway transport lines was collected using available data and using Eq. (1), the amount of annual CO₂ emissions resulting from the consumption of fossil fuels in the railway transport lines of the study area was calculated. Finally, to prepare a map of the annual distribution of carbon dioxide emissions resulting from this section, the total annual CO₂ emissions from the railway lines within Isfahan city were divided by the length of the railway lines in this area (Eq. (13), Table 2).

In order to prepare a spatial distribution map of carbon dioxide emissions in the agricultural sector, agricultural lands within the city of Isfahan were extracted from a city map at a scale of 1:2000, and the number of agricultural machinery and annual consumption of fossil fuels within the city area were collected. Then, the annual CO₂ emissions in this sector were calculated using Eq. (14) (Table 2). Finally, the total amount of CO₂ emissions annually was divided by the area of cultivated agricultural lands within the city of Isfahan. Finally, in the sixth stage, after calculating the spatial distribution map of carbon dioxide emissions resulting from the consumption of fossil fuels for each stationary and mobile source, all the spatial distribution maps of CO₂ emissions were overlaid on each other. The result of this integration shows the spatial distribution map of annual CO₂ emissions at the city level.

Transportation density results in the main and secondary arteries of the two-tiered roads indicate that the volume of cars on the main streets is 78% while it is 22% on the secondary and alleyways. This density was considered as the weight of each road type in the carbon dioxide emissions. Next, the weight calculated in the total amount of annual carbon dioxide emissions from fuel consumption in the road transport sector (excluding fuel consumption in the bus transport network) was multiplied. In this way, the amount of CO₂ was divided into two parts, the amount of CO₂ emitted from the main streets and secondary streets, which was calculated using Eqs. (6) and (7). The results showed that the amount of carbon dioxide emissions from transportation on main roads is 1,784,368.29 tons per year and on secondary roads is 503,283.36 tons per year.

Finally, the amount of carbon dioxide emissions in each section of the main roads was calculated using Eq. (8), which is shown on the spatial distribution map in Fig. 4. Fig. 4 also shows that in the first and second-degree arteries, around city squares and generally on roads with high hourly traffic, the amount of carbon dioxide emissions from fossil fuel combustion is also high. In general, the maximum amount of emissions of this gas on main streets is 621 kilograms per square meter per year in 2020. On the other hand, the distribution map of CO₂ emissions in secondary streets in neighbourhoods was calculated using Eq. (10), and its spatial distribution map is shown in Fig. 5. The results of the spatial distribution map of annual CO₂ emissions caused by fossil fuel combustion from light vehicles on secondary streets (Fig. 5) show that the minimum amount of emissions of this gas is 2.79 and the maximum amount is 119.44 kilograms per square meter.

The map of the distribution of carbon dioxide emissions in each section of public transportation lines was calculated using Eq. (12), and the result is presented in Fig. 6. The spatial distribution map of the annual emissions of CO₂ resulting from the combustion of fossil fuels in public transportation lines (Fig. 6) shows that the minimum and maximum levels of CO₂ emissions are 0.478 and 61.24 kilograms per square meter, respectively. The findings of this section of the study generally indicate that the amount of carbon dioxide emissions from the oxidation of hydrocarbons during the combustion process of fossil fuels on main and secondary streets in the urban area of Isfahan is 2,377,720.5 million tons per year, which accounts for 17.16% of the total carbon dioxide emissions from the combustion of fossil fuels in the city of Isfahan. Also, the total carbon dioxide emissions in the railway sector are 2844 tons in 2020. The annual distribution map of carbon dioxide emissions in this sector is shown in Fig. 7B.

The agricultural land area in the 15 districts of Isfahan city is approximately 13,724 hectares. According to the Isfahan City Statistical Yearbook, around 3450 pieces of agricultural machinery are active in these lands. Since, on average, each machine operates 1200 h per year and consumes 14 litres of fuel per hour, it can be stated that each agricultural machine consumes about 16,800 litres of fuel per year. The total diesel fuel consumption in the agricultural sector is 57.96 million litres per year. The total amount of carbon dioxide emissions from the agricultural transportation sector was 157,620.48 tons in 2020. Finally, to prepare the spatial distribution map of CO₂ emissions from agricultural lands, the total amount of annual CO₂ emissions were divided by the total agricultural land area in Isfahan city, and the result is presented in Fig. 7A. The spatial distribution map of CO₂ greenhouse gas emissions in the agricultural sector indicates that approximately 1.1485 kilograms of carbon dioxide are emitted into the atmosphere annually per square meter of agricultural lands in the 15 districts of Isfahan city.

The distribution maps of CO₂ emissions from each source were integrated by overlapping analysis. Fig. 8 illustrates the spatial distribution of annual carbon dioxide emissions in the city of Isfahan. Overall, this map shows that the amount of CO₂ emissions resulting from the oxidation of hydrocarbons during the combustion of fossil fuels in the Isfahan metropolitan area is 13,855,525.84 tons per year, with residential, commercial, industrial, power plant, road-rail transportation, and non-road transportation (agricultural machinery) activities contributing 21.78%, 4.92%, 4.37%, 50.61%, 17.18%, and 1.14% of the emitted carbon dioxide, respectively.

The study focuses on quantifying carbon dioxide (CO₂) emissions from fossil fuel combustion in Isfahan’s urban areas using Geographic Information Systems (GIS). It aims to address the challenge of assessing urban sustainability by analyzing CO₂ emissions from stationary and mobile sources. The research provides insights into emission patterns through data analysis and mapping techniques, aiding urban planners and policymakers in decision-making.

Urban CO₂ Emissions and Sustainability: This section explores how Geographic Information Systems (GIS) can be used to assess urban sustainability through the lens of CO₂ emissions from fossil fuel burning in Isfahan. Traditionally, such assessments lack precision. Our research offers a solution: a micro-scale analysis using GIS that pinpoints CO₂ emissions from both stationary (buildings) and mobile (vehicles) sources.

Micro-scale Approach and Data Analysis: Our study tackles the challenge of limited, imprecise methods for measuring CO₂ emissions in cities. We propose a novel approach using GIS to analyze data on fossil fuel consumption across various sectors (homes, businesses, factories, transportation). This allows us to quantify CO₂ emissions from both stationary and mobile sources, providing a detailed picture of Isfahan’s carbon footprint.

Key Findings and Emission Patterns: The analysis revealed interesting patterns in Isfahan’s fuel consumption and related CO₂ emissions. Homes were responsible for 21.78% of emissions, followed by industry (4.37%) and commerce (4.92%). Power plants, however, were the biggest contributor, responsible for a significant 50.61% of CO₂ emissions. We further investigated transportation, finding that road and rail together contributed 17.18% of emissions, while non-road sources (mainly agricultural machinery) accounted for 1.14%.

Mapping CO₂ Distribution: Using spatial distribution mapping, we visualized how CO₂ emissions vary across Isfahan’s geography. This revealed distinct “hotspots” of emissions, particularly in densely populated areas and along major transportation corridors. For example, CO₂ emissions from cars were higher on main roads compared to side streets. Similarly, emissions from public buses were concentrated on their designated routes.

A Comprehensive Picture: By combining findings from stationary and mobile sources, we created a comprehensive map that illustrates the total CO₂ emissions across Isfahan. This integrated approach allowed us to pinpoint areas with the highest carbon footprints, enabling targeted mitigation strategies. Notably, the analysis highlighted the outsized contribution of certain sectors, emphasizing the need for focused interventions to promote sustainability.

Theoretical Significance: Our study advances the theory of urban sustainability by demonstrating the effectiveness of GIS in quantifying and visualizing CO₂ emissions at a micro-scale level. By revealing the spatial distribution of emissions and their sectoral contributions, we offer valuable insights for urban planning and policy development. Furthermore, our methodology can be applied to other cities, facilitating comparisons and fostering a deeper understanding of how carbon dynamics work in urban environments.

Future Directions: In conclusion, this study provides a thorough analysis of CO₂ emissions from fossil fuel combustion in Isfahan. It highlights the usefulness of GIS in assessing urban sustainability. Our innovative methods and detailed spatial mapping offer valuable insights for policymakers and urban planners working to combat climate change and promote environmentally friendly development. Future research can build on our findings by incorporating additional data sources and refining spatial modeling techniques to create even more accurate and useful CO₂ emission assessments for cities.

Comparative Analysis of Carbon Dioxide Emission Mapping Methods:

Several methods exist for creating CO₂ emission maps, each with distinct strengths and weaknesses. This study explores three main approaches: satellite imagery, the ODIAC method, and the bottom-up (inventory) method.

Satellite Image-Based Method: This method utilizes satellite data to detect CO₂ emission sources based on factors like land use, vegetation changes, and thermal anomalies. The data is then processed to estimate emissions. However, its accuracy depends heavily on satellite resolution, atmospheric conditions, and the ability to distinguish natural from anthropogenic CO₂ sources. Additionally, it may struggle with detecting smaller or dispersed emissions [39].

ODIAC Method: The Open-source Data Inventory for Anthropogenic CO₂ (ODIAC) method combines various data sources like nightlights, population density, and industrial activity to estimate CO₂ emissions. Statistical models are then employed to allocate emissions to spatial grids. While ODIAC provides high-resolution global CO₂ emission maps, its accuracy can be limited by uncertainties in the input data and modeling assumptions. It may also struggle to represent emissions from rapidly changing industrial and urban areas [40].

Bottom-Up (Inventory) Method: This method involves collecting data on CO₂ emissions from various local or regional sources like industrial facilities, transportation, and energy consumption. This data is then aggregated to create a comprehensive inventory of emissions. The accuracy of this method hinges on the availability and quality of data reported by industries and government agencies. It can underestimate emissions from unreported sources and requires significant resources for data collection and processing [41].

Comparison and Discussion:

Satellite image-based methods and ODIAC offer spatially explicit CO₂ emission maps with global coverage, suitable for analyzing regional and global emission patterns. However, the inventory method provides more detailed and accurate emission estimates at local or sectoral levels, making it valuable for policy-making and mitigation strategies at those scales.

The inventory method stands out due to its direct data collection from various sources, leading to a more comprehensive and precise account of emissions at local or sectoral levels. This detailed breakdown empowers policymakers to target mitigation efforts effectively. Studies consistently demonstrate the inventory method’s superior accuracy and reliability, especially for smaller-scale mapping and emission reduction strategies. A recent study comparing CO₂ mapping methods further reinforces this, highlighting the inventory method’s suitability for local and regional contexts. By ensuring comprehensive coverage and direct data collection, the inventory method offers invaluable insights that can inform targeted policies and interventions aimed at reducing CO₂ emissions and combating climate change at local and regional levels.

Research Limitations:

This study confirms the limitations that can be considered in future research to further refine the spatial distribution of CO₂ emissions in urban areas. Acknowledging the limitations of this research, in order to map the spatial distribution of carbon dioxide emissions in this research, the data related to the amount of energy consumption in each residential, commercial and industrial building was not available separately. Therefore, we had to collect data related to the total amount of fossil fuels consumed annually in each of the sectors (i.e., residential, commercial and industrial sectors), which reduced the accuracy of this research. However, in case of access to the data of the amount of fossil fuel consumption in each building separately, the results of mapping the spatial distribution of CO₂ gas would be calculated much more accurately.

Here are some ways to promote such studies:

Collaboration with Utility Companies: Partnering with utility companies can provide access to individual building energy consumption data. This data can be anonymized to protect privacy while enabling researchers to map CO₂ emissions based on the specific energy use patterns of different building types (e.g., single-family homes, apartment buildings, office buildings).

Smart Meter Integration: The increasing adoption of smart meters in buildings offers a promising avenue for collecting real-time energy consumption data. Integrating smart meter data with GIS platforms can enable dynamic updates to CO₂ emission maps, reflecting actual energy use patterns and facilitating more responsive mitigation strategies.

Building Energy Modeling: Building energy modeling software can be employed to estimate energy consumption for individual buildings based on factors like building size, construction materials, and climate data. This approach can be particularly useful for buildings where actual consumption data is unavailable.

By incorporating these data sources, future research can create even more precise and actionable spatial distribution maps. These maps can then inform targeted interventions at the building level, such as retrofitting programs to improve energy efficiency or promoting the adoption of renewable energy sources like solar panels.

Achieved Objectives and Contribution to Urban Sustainability:

This study successfully achieved several key objectives that contribute to advancing urban sustainability in Isfahan and beyond. Firstly, it established a novel methodology for quantifying CO₂ emissions from fossil fuel combustion at a micro-scale level in an urban environment. This bottom-up approach, which analyzes data from individual sectors, provides a valuable alternative to traditional methods focusing on regional or national emissions.

Secondly, the study generated the first-ever spatial distribution map of CO₂ emissions for Isfahan, identifying hotspots associated with power plants, residential areas, and transportation corridors. This map serves as a crucial decision-making tool for urban planners and policymakers by pinpointing areas that require the most urgent attention for emission reduction strategies.

Thirdly, the study demonstrates the effectiveness of GIS technology in visualizing and analyzing CO₂ emissions data within an urban context. This paves the way for utilizing GIS in other cities to create similar spatial distribution maps, facilitating comparative analyses and the development of best practices for urban sustainability across different regions. Overall, this study contributes significantly to the field of urban sustainability by providing a replicable methodology, valuable data on CO₂ emissions in Isfahan, and a powerful visualization tool for informing future urban planning and policy decisions.