Allocation of Carbon Intensity Target Reduction Rate for China's 332 Cities Based on Entropy Method and Improved Equal-Proportion Distribution Method

Allocation of Carbon Intensity Target Reduction Rate for China's 332 Cities Based on Entropy Method and Improved Equal-Proportion Distribution Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Allocation of Carbon Intensity Target Reduction Rate for China's 332 Cities Based on Entropy Method and Improved Equal-Proportion Distribution Method Fengmei Yang, Yin Ren, Shudi Zuo, Jiaheng Ju, Meng Yang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6166405/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 14 Jan, 2026 Read the published version in Scientific Reports → Version 1 posted 9 You are reading this latest preprint version Abstract The rational allocation of carbon reduction targets is crucial for achieving the country's overall carbon reduction goal. This paper introduces a comprehensive carbon intensity reduction allocation scheme based on the entropy method and an improved equal-proportion distribution method (IEPD method), which integrates fairness and efficiency. Firstly, an indicator system including economic, demographic, energy, and technological innovation aspects is established, and the entropy method is employed to determine the weights of these indicators. Secondly, using the IEPD method, the carbon intensity reduction target for China's 14th Five-Year Plan period (namely, an 18% reduction in carbon intensity by 2025 compared to 2020) is allocated to 332 cities. Thirdly, K-means clustering is utilized to categorize the cities according to seven indicators, and the characteristics of the carbon intensity target reduction rate (CITRR) of each group are analyzed. The results show that: (1) The average CITRR of 332 cities is 13.13%, and the CITRR ranges from 2.76–88.58%. (2) The CITRR shows a step-like regional distribution difference that gradually decreases from the eastern region to the central and western regions, and the Global Moran I correlation index is 0.24, indicating a positive spatial correlation. (3) K-means clustering divides 332 cities into four categories, and the Kruskal-Wallis test shows a significant difference in the CITRR among the four categories of cities. The allocation plan proposed in this study can help cities assess their carbon intensity reduction capabilities and formulate effective policies. Earth and environmental sciences/Environmental social sciences Earth and environmental sciences/Environmental social sciences/Climate change impacts Earth and environmental sciences/Environmental social sciences/Climate change policy Carbon Intensity Reduction Target Allocation Fairness Efficiency Entropy Method The Improved Equal-Proportion Distribution Method Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1 Introduction Controlling carbon emissions to mitigate global warming has become a consensus among the international community (Glennerster and Jayachandran, 2023 ). China, the second most populous country in the world and a major economic power has the highest carbon emissions globally. To address this challenge, China has set the overarching goal of "achieving carbon peak by 2030 and carbon neutrality by 2060 ("dual carbon" goals) (Huang et al., 2025 )." In the pursuit of achieving the ultimate "dual carbon" goals, China has established specific carbon emission reduction targets for the "14th Five-Year Plan" period, namely "By 2025, carbon intensity will be 18% lower than in 2020.[i] ." These phased targets not only contribute to the realization of long-term visions but also provide clear direction and impetus for emission reduction efforts. The achievement of emissions reduction targets at the national level largely depends on the implementation strength and effectiveness at the local level (Zheng et al., 2024 ). The significant differences in regional resource distribution in China lead to disparities in emission reduction capabilities and responsibilities across regions, increasing the difficulty of allocating emission reduction quotas (Cheng et al., 2022 ). Therefore, how to equitably and rationally distribute carbon reduction targets to various regions and ensure fairness has become a question of significant research importance. This challenge requires comprehensively considering regional differences to formulate fair and effective reduction strategies. Carbon dioxide emissions from Chinese cities account for 85% of the national emissions, making them a key area for the implementation of carbon reduction policies (Lai et al., 2022 ). Moreover, a study by Wang et al. ( 2023 b) indicates that by 2030, nearly one-third of the cities may face the risk of failing to achieve their carbon peak targets (Wang et al., 2023 ). Thus, conducting carbon emission quota allocation in cities is crucial for aiding low-carbon construction and sustainable development. In the process of carbon allowance allocation, decision-makers formulate clear guiding principles based on the established reduction targets, thereby ensuring that each emission entity can obtain the corresponding emission quotas (Huang and Xu, 2020 ). Fairness, efficiency, and comprehensiveness are important principles in carbon allowance allocation (Bai and Li, 2024 ). The principle of fairness requires consideration of the differences between regions and ensures the allocation entities have equal status in terms of carbon allowance (Zhou et al., 2021 ). It is considered the most important allocation principle (Ju et al., 2021 ; Xie et al., 2020 ). The principle of fairness can be defined according to the allocation entities' emission reduction capabilities and responsibilities (Xia et al., 2023 ). Specifically, emission reduction capabilities are typically represented by indicators that reflect differences in socio-economic development, such as population, GDP, energy consumption, and other indicators (He, W. et al., 2021 ; Mi and Sun, 2021 ). Emission reduction responsibilities are usually reflected by historical cumulative carbon emissions (Jones et al., 2023 ) or the polluter pays principle (Ari and Sari, 2017 ). The principle of efficiency embodies the potential for emission reductions of the allocating entity (Chang et al., 2016 ). Greater carbon efficiency indicates higher economic output, while lower efficiency suggests more significant potential for future emission reductions (Xia et al., 2023 ). Therefore, allocation based on emission efficiency typically relies on indexes that gauge regional production efficiency, such as carbon intensity or efficiency metrics derived from DEA (Data Envelopment Analysis) (Cheng et al., 2022 ). A region with a low carbon intensity emits fewer greenhouse gases while generating the same economic value. Thus, it has a higher production efficiency. Efficiency measures based on DEA mainly draw on models such as SBM (Slacks-Based Measure) (Kao, 2024 ), CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) models (Smętek et al., 2022 ), and Directional Distance Function (Goyal et al., 2019 ). In summary, whether based on carbon intensity or quota optimization for efficiency, the principle of carbon allowance allocation is to allocate more allowances to regions with higher emission efficiency to enhance society's overall production efficiency. The principle of comprehensiveness refers to integrating multiple principles to accomplish the allocation task, which can effectively resolve the possible conflicts between different principles (Bai and Li, 2024 ). It allocates carbon emissions allowance by constructing a model that includes multiple indicators while considering economic development, social equity and environmental sustainability. For example, Zhou, et al. considered the historical transfer of carbon emissions and measured the cumulative net carbon emissions of each province in China following the principle of consumer responsibility, and devised a preliminary plan for allocating carbon allowances to each province in China for the year 2020, guided by the principles of fairness, efficiency, and sustainability (Zhou et al., 2021 ). Li et al. ( 2021 a) allocated CO 2 emission allowances for each province in China following the principles that combine equity, efficiency, feasibility, and sustainability (Li et al., 2021 ). Shojaei and Mokhtar ( 2022 ) used the DEA method to complete the allocation of carbon allowances among 26 countries, considering equity and efficiency. Their findings indicated that an allocation approach that accounts for regional heterogeneity is more rational.(Shojaei and Mokhtar, 2022 ). Commonly used carbon allowance allocation methods include DEA methods (Bai et al., 2024 ; Liu et al., 2024 ), shadow price allocation methods (Ao et al., 2023 ), game theory methods (Zhang et al., 2014 ), and indicator methods. Among them, DEA focuses too much on efficiency, resulting in a lack of fairness and rationality, which is easily questioned (Chen et al., 2020 ). The shadow price allocation method relies on an empirical model solution with a large number of parameter estimates, which is data-demanding and computationally complex (Ao et al., 2023 ). Game theory methods are complex to operate, and their transparency and feasibility are debatable (Chatterjee and Sabourian, 2009 ). Indicator methods are generally used in combination with other methods. When constructing an indicator system, the entropy method is widely used because it can consider various principles, including fairness, feasibility, efficiency, and sustainability, during combining multiple indicators. It also helps to avoid the issue of subjective weights being influenced by the decision-maker's subjectivity (Li et al., 2022 ; Li et al., 2021 ).When conducting carbon allowance allocation among cities, it is crucial to consider the differences in the socio-economic resource conditions of each city to ensure that the program is fair and efficient. At the same time, the large number of cities makes it difficult to obtain indicator data, and a model with high data requirements cannot be applied. For this reason, this study introduces an improved equal-proportion distribution method (IEPD method) to realize differential allocation. The IEPD method can be appropriately adjusted according to the differences among various regions, based on the overall average reduction, so that the emission reduction tasks assigned to each region are well-suited to their specific conditions, thereby demonstrating strong practical applicability (Shi, L. et al., 2020 ). To summarize, carbon allowance allocation is a complex decision-making process. This study proposes a comprehensive methodological system to make this process fair and efficient. First, emphasizing the balance between fairness and efficiency, an extensive system of indicators affecting carbon intensity is constructed by integrating the capabilities and responsibilities of various cities using the entropy method. This step can objectively reflect the emission reduction capacity of each city. Second, an IEPD method is employed to allocate the carbon intensity reduction targets for China's 14th Five-Year Plan period to 332 cities. Based on the overall average reduction rate, this method makes appropriate adjustments following the specific circumstances of each region, ensuring that the carbon intensity target reduction rate (CITRR) undertaken by each region matches its conditions. Finally, the K-means cluster is used to categorize cities based on the seven indicators and to study the distribution characteristics of CITRR among different categories of cities. This step helps us understand the differences and needs of various groups of cities regarding their carbon intensity reduction targets. The most significant contribution of this study lies in establishing a coupled model that combines fairness and efficiency for allocating the carbon intensity reduction targets for 332 cities in China. This model considers multiple influencing indicators in allocating carbon emission reduction targets, considers regional differences, and is readily accepted by all parties. 2 Data and method 2.1 Technical route of the research As shown in Fig. 1 , the technical route of this study includes four steps: Step 1: Constructing an evaluation indicator system that affects carbon intensity from four intangible production factors: economy, demographic, energy, and technological innovation. Step 2: Assessing the weight values of each indicator through the entropy method and calculating the CITRR for 332 cities in China by the IEPD method. Step 3: Visualizing the CITRR for 332 cities of China in ArcGIS 10.8 and analyzing the CITRR’s results. Step 4: Clustering 332 cities based on their indicator characteristics using the K-means clustering method and analyzing the characteristics of CITRR under different clusters to provide corresponding emission reduction recommendations. 2.2 Construction of evaluation indicator system The principle of fairness requires that regional carbon allowance adapt to the level of regional development. In this research, economic and demographic factors are used as representatives of the scale of regional development. The economic factor includes the level of economic development and the industrial structure. Per capita GDP serves as an indicator of the level of economic development, while the secondary industry in GDP reflects the industrial structure. These indicators positively correlate with regional carbon allowance (Shi, L. et al., 2020 ). The demographic factors include both population size and demographic structure. Among them, the population size is expressed by the permanent population, and the population size affects the scale of demand and production, which then affects CO 2 emissions. Hence, the permanent population is a positive indicator. The urbanization rate represents demographic structure. Urbanization increases energy efficiency and reduces the opportunity for CO 2 emissions (Huang, 2018 ), making it a negative indicator (Table 1 ). The efficiency principle requires that in allocating carbon allowances, the goal is to attain the highest economic return with the least amount of resource input, thereby achieving the optimal allocation of resources (Zhou et al., 2021 ). This study uses energy and technological innovation factors to represent the efficiency principle. Due to the challenge of acquiring energy data at the city level, electricity consumption is routinely used as a surrogate for overall energy consumption (Xiufan and Decheng, 2023 ). Therefore, this study uses the electricity consumption per 10,000 yuan as an indicator to reflect the impact of energy factors on carbon intensity. In China, power generation is predominantly thermal-based, which is heavily reliant on coal and fossil fuels (Zhang, 2019 ). Hence, this indicator is a positive one. The technological innovation factor is indicated by the number of patent grants and the proportion of scientific and educational expenditures in the total fiscal expenditure. Research and development investment affects technological change, and according to relevant studies, technological change is currently a positive indicator of carbon intensity in China (Shi, L. et al., 2020 ). Table 1 Indicator system affecting carbon intensity Affecting Factors Indicators Abbreviation Indicators’ Attribute Economic factors Per capita GDP PGDP + Secondary industry in GDP SIP + Demographic factors Permanent population PP + Urbanization rate UR - Energy factors Electricity consumption per 10,000 yuan EC + Technological innovation factors Number of patent grants PG + Proportion of scientific and educational expenditures PSEE + Note: “+” indicates an increase in carbon intensity with an increase in the indicator value, while “−” indicates a decrease in carbon intensity with an increase in the indicators value. 2.3 Method 2.3.1 Entropy method The entropy method serves as an integrated indicator approach capable of consolidating multiple criteria that represent diverse allocation principles (Cui et al., 2020; He, D. et al., 2021 ). Which determine weight indicators through the transmission of information quantity, calculate entropy values to reflect utility value, and thus obtain more reliable weights. Therefore, the entropy method is an objective approach to determining the degree of dispersion of each indicator, unaffected by the subjective influence of decision-makers (Wang et al., 2019 ). The steps of the entropy method are as follows. Firstly, the raw data need to be normalized. The normalized methods for positive indicators and negative indicators are respectively shown in formulas (1) and (2). Positive indicator: \(\:{X}_{ij}=\frac{{x}_{ij}-{min}_{j}}{{max}_{j}-{min}_{j}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(1\right)\) Negative indicator: \(\:{X}_{ij}=\frac{{max}_{j}-{x}_{ij}}{{max}_{j}-{min}_{j}}\) (2) Where X ij represents the normalized result of the \(\:j\) th indicator of city \(\:i\) ; x ij represents the original value of the \(\:j\) th indicator of city \(\:i\) ; max j represents the maximum original value of the j th indicator; min i represents the minimum original value of the i th indicator. The ratio of X ij to the sum of 332 cities of the \(\:j\:\) th indicator ( P ij ) is calculated as follows: $$\:{P}_{ij}=\frac{{X}_{ij}}{{\sum\:}_{i=1}^{n}{X}_{ij}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(3\right)$$ When the differences in indicator values are greater, more useful information can be obtained from these differences, but the entropy value is smaller. Secondly, based on the calculations, the weight calculation formulas for the seven indicators of the 332 studied cities are shown below. $$\:{e}_{j}=\frac{{\sum\:}_{i=1}^{n}{p}_{ij}\text{ln}{p}_{ij}}{-\text{ln}n}$$ 4 where if p ij is 0, then p ij ln p ij also is defined as 0. Thirdly, the weight of each indicator can be computed: $$\:{W}_{j}=\frac{1-{e}_{j}}{{\sum\:}_{j=1}^{m}(1-{e}_{j})}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(5\right)$$ Where the information entropy value of indicator \(\:j\) is represented by e j , and W j is the weight of the \(\:j\) th indicator. 2.3.2 IEPD method The IEPD method focuses on "average reduction" and "relative reduction" during the distribution reduction process, including two variables: the average reduction rate and the relative reduction factor. The average reduction rate indicated the standard for proportional distribution, while the relative reduction factor served as a suitable adjustment following a set of fairness criteria. The CITRR in each city is calculated by the average reduction rate and the relative reduction factor (Shi, Longyu et al., 2020). In the IEPD method calculating process, the relative reduction factor α i needs to be determined based on the CITRR allocation indicator system, reflecting each city's differentiated emission reduction responsibilities based on proportional allocation. The calculation formula is as follows. $$\:{\alpha\:}_{i}=\frac{\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}{\frac{1}{n}\sum\:_{i=1}^{n}\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}\left(n=1,\dots\:,332;m=1,\dots\:,7\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(6\right)$$ where Z ij represents the normalized value of the j th indicator for the i th city, W j is the weight of the j th indicator. The average CITRR of each city reflects the concept of equal distribution, which is calculated based on the overall target reduction rate C required at the national level and the relative reduction factors of each city. The formula is as follows: $$\:\stackrel{-}{x}=\frac{C\sum\:_{i=1}^{n}{G}_{i}{I}_{i}}{\sum\:_{i=1}^{n}{G}_{i}{I}_{i}{\alpha\:}_{i}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(7\right)$$ Where \(\:\stackrel{-}{x}\:\) is the average CITRR for 332 cities. I i represents the carbon intensity of city i in 2020, and Gi represents the GDP of city i in 2025. Finally, the CITRR for city i , namely \(\:{x}_{i},\:\) is given by the formula: $$\:{x}_{i}=\frac{C\sum\:_{i=1}^{n}{G}_{i}{I}_{i}}{\sum\:_{i=1}^{n}(\frac{\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}{\frac{1}{n}\sum\:_{i=1}^{n}\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}\times\:{G}_{i}{I}_{i})}\times\:\frac{\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}{\frac{1}{n}\sum\:_{i=1}^{n}\sum\:_{j=1}^{m}{Z}_{ij}\times\:{W}_{j}}\:\:\:\:\:\:\:\:\:\left(8\right)$$ 2.3.3 K-means clustering method The K-means clustering method is a classical clustering method with many applications. The results are presented in clusters, each containing a set of data points with similar characteristics. Such clustering outcomes are intuitive and easy to understand, facilitating interpretation and presentation. The clustering step of K-means consists of four steps (Li et al., 2023 ; Moradi Fard et al., 2020 ): (1) Using the elbow method or other methods to determine the optimal number of clusters (k). In this research, the elbow method result shows that the k is four after normalizing indicator values. (2) Randomly selecting four data points as the initial cluster centers, calculating the distance from each data point to each cluster center, and assigning each data point to the cluster corresponding to the nearest cluster center. (3) Recalculate each cluster's cluster centers, typically using the mean of all data points within the cluster as the new cluster center. (4) Repeating the second and third steps until the cluster centers no longer change. 2.4 Data source and processing In this study, the carbon intensity of cities is sourced from the "China City CO 2 Emission Dataset" (2020), whereas other socio-economic data are collected from the respective city statistical yearbooks (2021). This study employs the GM (1,1) model for GDP forecasting. Due to the large number of cities, when conducting the first round of GM (1,1) prediction from 2010–2023, spanning 14 years, the prediction results of some cities were in the third and fourth-level grades. To improve the prediction results, the study selected these cities to carry out the second prediction round, and shortened the period to 2016–2023, spanning 8 years. The results of the first prediction show that 254 cities achieved a first-level accuracy grade, 20 cities achieved a second-level accuracy grade, 17 cities achieved a third-level accuracy grade, and 41 cities achieved a fourth-level accuracy grade. Therefore, the second prediction selected 58 cities from the third and fourth-level accuracy grades for prediction. The prediction results show that 50 cities achieved a first-level accuracy grade, 4 cities achieved a second-level accuracy grade, and 4 cities achieved a third-level accuracy grade. GM (1,1) prediction accuracy grades are shown in Table 2 . Table 2 GM (1,1) prediction accuracy grades Grades Accuracy C (Mean squared error ratio) P (Small error probability) First-level Good C ≤ 0.35 ≥ 0.95 Second-level Qualified 0.35<C ≤ 0.50 0.80 ≤ P<0.95 Third-level Marginally 0.50<C ≤ 0.65 0.70 ≤ P0.65 <0.70 3 Results 3.1 Indicators’ weights The objective weights of each indicator were calculated according to formula (5), as shown in Table 3 . It can be seen that the weight of the EC indicator was the largest, W EC =0.407, indicating that in the allocation of carbon intensity, the differences in electricity consumption per 10,000 yuan were given the highest priority. PG factor followed, W PG =0.382. As calculated, the PP factor's weight was close to only a quarter of the EC factor. It ranked as the third highest among the seven types of factors (0.107). The weight values of the remaining four factors were all below 0.1, among which the PSEE factor has the lowest weight value, W PSEE =0.011, indicating that in the allocation of carbon intensity, the differences in the proportion of science and education expenditure to total fiscal expenditure were considered less important. The weight of the SIP factor is close to that of the PSEE, at 0.015. The weight values for UR and PGDP were 0.024 and 0.055, respectively. Table 3 The weights of the seven indicators Factors PDGP SIP PP UR EC PG PSEE Weight 0.055 0.015 0.107 0.024 0.407 0.382 0.011 3.2 CITRR results Under the target constraint set by China's "14th Five-Year Plan" to achieve an 18% reduction in carbon intensity by 2025 compared to 2020, calculations based on formula 7 yield an average CITRR of 13.13%. Furthermore, considering the weight of the seven influencing factors, the CITRR assigned to individual cities exhibits notable variations, ranging from 2.76–88.58%. Figure 2 shows cities with low CITRR located in China's border areas (the three northeastern provinces, Xinjiang, Tibet, and Yunnan) and cities with high CITRR distributed along the coastal cities. The target reduction rate for central cities tends to be at an intermediate level. By calculating the spatial autocorrelation of the CITRR, the Global Moran I correlation index is 0.24, with a p-value equal to 0, proving that the distribution of CITRR among the 332 cities exhibits spatial effects. Specifically, Shenzhen topped the list with a CITRR of 88.58%. Yushu Tibetan Autonomous Prefecture, Shanghai, Guangzhou, and Beijing followed closely behind, with CITRR of 78.99%, 72.44%, 67.84%, and 66.85%, respectively. This result was closely related to Shenzhen, Shanghai, Guangzhou, and Beijing's status as one of China's economic special zones, with a high level of economic development, the highest urbanization rate, and the largest number of patent authorizations among all cities, thus bearing the greatest task of carbon intensity reduction. However, the reasons for Yushu Tibetan Autonomous Prefecture's second-highest ranking in CITRR are unclear. In contrast, the Daxing'anling region had the lowest CITRR, at only 2.76%. The cities ranking second to fifth from the bottom in terms of CITRR were Yichun, Hegang, Qitaihe, and Jixi, with 4.02%, 4.99%, 5.07%, and 5.24%. It was noteworthy that all of the aforementioned five cities are located in Heilongjiang Province, and this aligns with its ecologically sensitive function as one of China's key state-owned forest areas and primary distribution areas for natural forests. The region had an average level of economic development, and its electricity consumption per 10,000 yuan, which carries the greatest weight, was the smallest among all cities. Hence, its CITRR was the lowest. 3.3 CITRR results in different types of cities K-means clustering was applied to divide the 332 cities into four clusters, and the spatial distribution of the four clusters of cities is shown in Fig. 3 . Cluster 1 includes 77 cities, such as Harbin, Haikou, and Sanya, as well as some autonomous cities of ethnic minorities. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.152, SIP: 0.544, PP: 0.134, UR: 0.476, PG: 0.018, PSEE: 0.635, EC: 0.007 (Fig. 4 ). The Liangshan Yi Autonomous Prefecture is the area closest to the cluster center among these cities. Cluster 1 cities’ specific characteristics are that the secondary industry in GDP is relatively low, and the proportion of scientific and educational expenditures is also low in the four types of clustered cities. However, the electricity consumption per 10,000 yuan is the highest. Cluster 2 includes 117 cities, such as Shijiazhuang, Handan, Huanggang, and others. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.131, SIP: 0.36, PP: 0.056, UR: 0.513, PG: 0.005, PSEE: 0.425, EC: 0.027. The Kashgar region is the area closest to the cluster center among these cities. Compared to the other three types of cities, it has the second-highest permanent population and the second-highest proportion of scientific and educational expenditures. Cluster 3 includes 111 cities, such as Changchun, Taiyuan, Yantai. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.527, SIP: 0.57, PP: 0.379, UR: 0.817, PG: 0.334, PSEE: 0.716, EC: 0.003. Yancheng is the closest to the cluster center. This type of city's characteristic is that its per capita GDP is higher than cluster 1 and cluster 2 but slightly lower than cluster 4. Its secondary industry in GDP is the highest among the four types of cities. Cluster 4 includes 27 cities, such as Beijing, Shanghai, and Wuhan. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.316, SIP: 0.678, PP: 0.1, UR: 0.663, PG: 0.036, PSEE: 0.57, EC: 0.009. Guangzhou is the city closest to the cluster center. The characteristic of this type of city is a higher proportion of scientific and educational expenditures. However, it has the lowest electricity consumption per 10,000 yuan among the four categories of cities. The Kruskal-Wallis test, the P < 0.001, indicates a significant difference in the CITRR among the four categories of cities. The range of CITRR for cluster 1 is 2.76–10.01%; for cluster 2, it is 6.84–15.33%; for cluster 3, it is 7.23–21.56%, for cluster 4, it is 18.56–88.58% (Fig. 5 ). As for the cities closest to the cluster centers in each cluster, the city with the lowest CITRR is Guangzhou, in cluster 4, with a CITRR of 11.39%. The CITRR for Yancheng in cluster 3 and Kashgar region in cluster 4 are very close, consistent with the overall distribution characteristics of CITRR for these two categories of cities, at 18.59% and 15.57%, respectively. In contrast, the city with the highest CITRR is Liangshan Yi Autonomous Prefecture in cluster 1, with a CITRR nearly twice that of Guangzhou, reaching 20.01%. 4 Discussions In the process of allocating carbon intensity reduction targets, equity and efficiency are complementary (Pan et al., 2023 ). Efficiency without equity can lead to certain regions bearing a disproportionate burden, potentially undermining social cohesion and political support for climate policies. Conversely, equity without efficiency may increase overall costs and slow progress toward emission reduction targets. To reconcile these two principles, this study uses the decline in carbon intensity as an observation indicator, constructs multiple influencing factors such as economic, demographic, energy, and technological innovation, employs the entropy method to obtain the weights of the indicators, and introduces an IEPD method to obtain the CITRR for various cities during the 14th Five-Year Plan period. This research shows that balancing equity and efficiency in allocating carbon intensity reduction targets is crucial. Scientific methods and models can optimize the allocation, ensuring the reasonable development of each region and the fair sharing of emission reduction responsibilities. Carbon intensity exhibits a significant regional clustering trend (Pang et al., 2020 ; Zhao et al., 2023 ). This study further confirms that the CITRR also has spatial characteristics, meaning regions with higher CITRR tend to be adjacent to regions with similarly high reduction targets. As shown in Fig. 2 , the CITRR in coastal developed areas is significantly higher than inland areas, gradually decreasing from the eastern to the central and western regions. The eastern region of China, especially the coastal areas, demonstrates a higher economic scale, growth rate, and industrial strength, making it China's most economically active and developed region. Regions with higher levels of economic development are more inclined to adopt advanced emission reduction technologies and management measures, thus forming a spatial clustering effect of high carbon reduction rates (Guo and Yu, 2024 ). Therefore, when formulating and implementing carbon reduction policies, it is necessary to encourage all regions to jointly set carbon reduction targets and policies to promote governance collaboration while considering the differences between regions and adopting differentiated and targeted measures to achieve more effective carbon reduction goals. The limitation of this study lies in the insufficient consideration of the impact of policy factors on emission reduction tasks. Policy factors include but are not limited to, local government emission reduction policies, incentive measures, regulatory restrictions, and the adoption of new technologies, all of which can significantly affect the completion of urban emission reduction tasks. For instance, a city with stricter environmental regulations and incentive policies may more effectively promote the implementation of emission reduction measures, thereby taking on more responsibility in emission reduction tasks. Conversely, suppose a city lacks sufficient policy support, even if it has a more significant potential for emission reduction. In that case, it may struggle to achieve its expected emission reduction targets due to inadequate policy incentives. Therefore, to allocate emission reduction tasks more accurately, future research needs to consider policy factors and develop more scientifically sound and reasonable schemes, ensuring the tasks' fairness and effectiveness while promoting the enthusiasm and innovation of various cities in the emission reduction process. 5 Conclusions and recommendations 5.1 Conclusions The weights of seven indicators affecting carbon emissions intensity, calculated using the entropy Method, are ranked from highest to lowest: EC, PG, PP, PGDP, UR, SIP, and PSEE. The IEPD method is used to calculate the CITRR, and the results of 332 cities show that the city with the highest CITRR is Shenzhen. At the same time, the lowest is the Daxing'anling region. Geographically, high CITRR cities are distributed in coastal areas, while low CITRR mainly sites in border regions, primarily in Heilongjiang Province, Xinjiang, and the Tibet Autonomous Region. Furthermore, according to the spatial autocorrelation regression analysis, the CITRR's Global Moran I correlation index is 0.24, which means that the CITRR of the 332 cities exhibits spatial effects. Finally, based on their indicators characteristics, the 332 cities are divided into four clusters by the K-means clustering method, and the differences in CITRR among each cluster of cities are significant. 5.2 Recommendations Due to the differences in characteristics among the four categories of cities, the CITRR varies across each category. This study provides policy recommendations for each category of city, respectively. Cluster 1 belongs to those with relatively low levels of economic development, which implies a weaker capacity in allocating carbon intensity. Consequently, the CITRR is significantly lower. These cities should enhance their level of industrialization and increase investment in scientific research to develop high-tech industries, thereby improving their economic growth model. The CITRR of cluster 2 and cluster 3 are relatively close, indicating their similar comprehensive capabilities in reducing carbon intensity. Cluster 2, building on its high proportions of permanent population and scientific and educational expenditures, should further optimize the population structure and allocation of scientific and educational resources to enhance the efficiency of such expenditures. Cluster 3, while maintaining the stable development of the secondary industry, should focus on developing the tertiary sector, including the service industry and high-tech industries, to increase the diversification of the economy. Cluster 4 represents the top tier of comprehensive development, encompassing the most advanced cities in the country, which have a high degree of economic development. Consequently, the CITRR is significantly higher. These cities can leverage their economic development advantages to promote carbon finance operations, such as carbon quota trading, investment and financing, as well as bank loans. Declarations Funding This work was supported by the National Natural Science Foundation of China 42001210. Data availability statement The datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Contact email: [email protected] CRediT authorship contribution statement Fengmei Yang: Writing – original draft, Resources, Methodology, Investigation. Yin Ren: Project administration, Conceptualization. Shudi Zuo: Funding acquisition. Jiaheng Ju: Formal analysis, Software, Data curation. Meng Yang: Writing – review & editing. 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Zhou, H., Ping, W., Wang, Y., Wang, Y., Liu, K. 2021. “China’s initial allocation of interprovincial carbon emission rights considering historical carbon transfers: Program design and efficiency evaluation”. Ecol. Ind. 121, 106918. https://doi.org/10.1016/j.ecolind.2020.106918. Footnotes https://www.gov.cn/zhengce/content/2021-10/26/content_5644984.htm Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6166405","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":436200430,"identity":"74c75ccf-0b9e-4fa2-97ce-9d48361f60d9","order_by":0,"name":"Fengmei Yang","email":"","orcid":"","institution":"Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Fengmei","middleName":"","lastName":"Yang","suffix":""},{"id":436200431,"identity":"28ca9af0-11d9-4cbf-86ec-8159545b1a87","order_by":1,"name":"Yin Ren","email":"","orcid":"","institution":"Chinese Academy of 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1","display":"","copyAsset":false,"role":"figure","size":192043,"visible":true,"origin":"","legend":"\u003cp\u003eFlow chart of this study\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/562220e0f32d7be77ff66b22.png"},{"id":80326522,"identity":"4cb78f07-a7e2-4e97-b978-3116ed223d5d","added_by":"auto","created_at":"2025-04-10 14:27:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":329055,"visible":true,"origin":"","legend":"\u003cp\u003eCITRR distribution map\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/e117d97f6dbc23d02ff9b17e.png"},{"id":80326805,"identity":"6496a9d7-37c9-40a4-8fc2-3652026ee8b5","added_by":"auto","created_at":"2025-04-10 14:35:55","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":325445,"visible":true,"origin":"","legend":"\u003cp\u003eThe geographical distribution of the four clusters of cities\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/8006ab5371a2b3bc08f68334.png"},{"id":80327597,"identity":"474bf0cb-7499-44c1-a7a0-ecc1ca195288","added_by":"auto","created_at":"2025-04-10 14:43:55","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":216563,"visible":true,"origin":"","legend":"\u003cp\u003eThe normalized values of the indicators for each city cluster center\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/25004ba96969fb2577dac1e2.png"},{"id":80326804,"identity":"57479329-172a-46a4-9f72-f5891eddf71e","added_by":"auto","created_at":"2025-04-10 14:35:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":98793,"visible":true,"origin":"","legend":"\u003cp\u003eThe violin and box plots of CITRR for each cluster of cities\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/3cf3983ec3169dfb0decfe69.png"},{"id":100614606,"identity":"96caf54a-1beb-4eda-a9eb-6ff718f0c5f9","added_by":"auto","created_at":"2026-01-19 17:22:19","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1918643,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6166405/v1/b55c798c-9ef6-4866-aba1-9776a8c85229.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Allocation of Carbon Intensity Target Reduction Rate for China's 332 Cities Based on Entropy Method and Improved Equal-Proportion Distribution Method","fulltext":[{"header":"1 Introduction","content":"\u003cp\u003eControlling carbon emissions to mitigate global warming has become a consensus among the international community (Glennerster and Jayachandran, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). China, the second most populous country in the world and a major economic power has the highest carbon emissions globally. To address this challenge, China has set the overarching goal of \"achieving carbon peak by 2030 and carbon neutrality by 2060 (\"dual carbon\" goals) (Huang et al., \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2025\u003c/span\u003e).\" In the pursuit of achieving the ultimate \"dual carbon\" goals, China has established specific carbon emission reduction targets for the \"14th Five-Year Plan\" period, namely \"By 2025, carbon intensity will be 18% lower than in 2020.[i]\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e\u003c/a\u003e.\" These phased targets not only contribute to the realization of long-term visions but also provide clear direction and impetus for emission reduction efforts.\u003c/p\u003e \u003cp\u003eThe achievement of emissions reduction targets at the national level largely depends on the implementation strength and effectiveness at the local level (Zheng et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The significant differences in regional resource distribution in China lead to disparities in emission reduction capabilities and responsibilities across regions, increasing the difficulty of allocating emission reduction quotas (Cheng et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Therefore, how to equitably and rationally distribute carbon reduction targets to various regions and ensure fairness has become a question of significant research importance. This challenge requires comprehensively considering regional differences to formulate fair and effective reduction strategies. Carbon dioxide emissions from Chinese cities account for 85% of the national emissions, making them a key area for the implementation of carbon reduction policies (Lai et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Moreover, a study by Wang et al. (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003eb) indicates that by 2030, nearly one-third of the cities may face the risk of failing to achieve their carbon peak targets (Wang et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Thus, conducting carbon emission quota allocation in cities is crucial for aiding low-carbon construction and sustainable development.\u003c/p\u003e \u003cp\u003eIn the process of carbon allowance allocation, decision-makers formulate clear guiding principles based on the established reduction targets, thereby ensuring that each emission entity can obtain the corresponding emission quotas (Huang and Xu, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Fairness, efficiency, and comprehensiveness are important principles in carbon allowance allocation (Bai and Li, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe principle of fairness requires consideration of the differences between regions and ensures the allocation entities have equal status in terms of carbon allowance (Zhou et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). It is considered the most important allocation principle (Ju et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Xie et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The principle of fairness can be defined according to the allocation entities' emission reduction capabilities and responsibilities (Xia et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Specifically, emission reduction capabilities are typically represented by indicators that reflect differences in socio-economic development, such as population, GDP, energy consumption, and other indicators (He, W. et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Mi and Sun, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Emission reduction responsibilities are usually reflected by historical cumulative carbon emissions (Jones et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) or the polluter pays principle (Ari and Sari, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe principle of efficiency embodies the potential for emission reductions of the allocating entity (Chang et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Greater carbon efficiency indicates higher economic output, while lower efficiency suggests more significant potential for future emission reductions (Xia et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Therefore, allocation based on emission efficiency typically relies on indexes that gauge regional production efficiency, such as carbon intensity or efficiency metrics derived from DEA (Data Envelopment Analysis) (Cheng et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). A region with a low carbon intensity emits fewer greenhouse gases while generating the same economic value. Thus, it has a higher production efficiency. Efficiency measures based on DEA mainly draw on models such as SBM (Slacks-Based Measure) (Kao, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) models (Smętek et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2022\u003c/span\u003e), and Directional Distance Function (Goyal et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). In summary, whether based on carbon intensity or quota optimization for efficiency, the principle of carbon allowance allocation is to allocate more allowances to regions with higher emission efficiency to enhance society's overall production efficiency.\u003c/p\u003e \u003cp\u003eThe principle of comprehensiveness refers to integrating multiple principles to accomplish the allocation task, which can effectively resolve the possible conflicts between different principles (Bai and Li, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). It allocates carbon emissions allowance by constructing a model that includes multiple indicators while considering economic development, social equity and environmental sustainability. For example, Zhou, et al. considered the historical transfer of carbon emissions and measured the cumulative net carbon emissions of each province in China following the principle of consumer responsibility, and devised a preliminary plan for allocating carbon allowances to each province in China for the year 2020, guided by the principles of fairness, efficiency, and sustainability (Zhou et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Li et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003ea) allocated CO\u003csub\u003e2\u003c/sub\u003e emission allowances for each province in China following the principles that combine equity, efficiency, feasibility, and sustainability (Li et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Shojaei and Mokhtar (\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) used the DEA method to complete the allocation of carbon allowances among 26 countries, considering equity and efficiency. Their findings indicated that an allocation approach that accounts for regional heterogeneity is more rational.(Shojaei and Mokhtar, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eCommonly used carbon allowance allocation methods include DEA methods (Bai et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Liu et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), shadow price allocation methods (Ao et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), game theory methods (Zhang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), and indicator methods. Among them, DEA focuses too much on efficiency, resulting in a lack of fairness and rationality, which is easily questioned (Chen et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The shadow price allocation method relies on an empirical model solution with a large number of parameter estimates, which is data-demanding and computationally complex (Ao et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Game theory methods are complex to operate, and their transparency and feasibility are debatable (Chatterjee and Sabourian, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2009\u003c/span\u003e). Indicator methods are generally used in combination with other methods. When constructing an indicator system, the entropy method is widely used because it can consider various principles, including fairness, feasibility, efficiency, and sustainability, during combining multiple indicators. It also helps to avoid the issue of subjective weights being influenced by the decision-maker's subjectivity (Li et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Li et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).When conducting carbon allowance allocation among cities, it is crucial to consider the differences in the socio-economic resource conditions of each city to ensure that the program is fair and efficient. At the same time, the large number of cities makes it difficult to obtain indicator data, and a model with high data requirements cannot be applied. For this reason, this study introduces an improved equal-proportion distribution method (IEPD method) to realize differential allocation. The IEPD method can be appropriately adjusted according to the differences among various regions, based on the overall average reduction, so that the emission reduction tasks assigned to each region are well-suited to their specific conditions, thereby demonstrating strong practical applicability (Shi, L. et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eTo summarize, carbon allowance allocation is a complex decision-making process. This study proposes a comprehensive methodological system to make this process fair and efficient. First, emphasizing the balance between fairness and efficiency, an extensive system of indicators affecting carbon intensity is constructed by integrating the capabilities and responsibilities of various cities using the entropy method. This step can objectively reflect the emission reduction capacity of each city. Second, an IEPD method is employed to allocate the carbon intensity reduction targets for China's 14th Five-Year Plan period to 332 cities. Based on the overall average reduction rate, this method makes appropriate adjustments following the specific circumstances of each region, ensuring that the carbon intensity target reduction rate (CITRR) undertaken by each region matches its conditions. Finally, the K-means cluster is used to categorize cities based on the seven indicators and to study the distribution characteristics of CITRR among different categories of cities. This step helps us understand the differences and needs of various groups of cities regarding their carbon intensity reduction targets.\u003c/p\u003e \u003cp\u003eThe most significant contribution of this study lies in establishing a coupled model that combines fairness and efficiency for allocating the carbon intensity reduction targets for 332 cities in China. This model considers multiple influencing indicators in allocating carbon emission reduction targets, considers regional differences, and is readily accepted by all parties.\u003c/p\u003e"},{"header":"2 Data and method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Technical route of the research\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, the technical route of this study includes four steps:\u003c/p\u003e \u003cp\u003eStep 1: Constructing an evaluation indicator system that affects carbon intensity from four intangible production factors: economy, demographic, energy, and technological innovation.\u003c/p\u003e \u003cp\u003eStep 2: Assessing the weight values of each indicator through the entropy method and calculating the CITRR for 332 cities in China by the IEPD method.\u003c/p\u003e \u003cp\u003eStep 3: Visualizing the CITRR for 332 cities of China in ArcGIS 10.8 and analyzing the CITRR\u0026rsquo;s results.\u003c/p\u003e \u003cp\u003eStep 4: Clustering 332 cities based on their indicator characteristics using the K-means clustering method and analyzing the characteristics of CITRR under different clusters to provide corresponding emission reduction recommendations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Construction of evaluation indicator system\u003c/h2\u003e \u003cp\u003eThe principle of fairness requires that regional carbon allowance adapt to the level of regional development. In this research, economic and demographic factors are used as representatives of the scale of regional development. The economic factor includes the level of economic development and the industrial structure. Per capita GDP serves as an indicator of the level of economic development, while the secondary industry in GDP reflects the industrial structure. These indicators positively correlate with regional carbon allowance (Shi, L. et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The demographic factors include both population size and demographic structure. Among them, the population size is expressed by the permanent population, and the population size affects the scale of demand and production, which then affects CO\u003csub\u003e2\u003c/sub\u003e emissions. Hence, the permanent population is a positive indicator. The urbanization rate represents demographic structure. Urbanization increases energy efficiency and reduces the opportunity for CO\u003csub\u003e2\u003c/sub\u003e emissions (Huang, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), making it a negative indicator (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe efficiency principle requires that in allocating carbon allowances, the goal is to attain the highest economic return with the least amount of resource input, thereby achieving the optimal allocation of resources (Zhou et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). This study uses energy and technological innovation factors to represent the efficiency principle. Due to the challenge of acquiring energy data at the city level, electricity consumption is routinely used as a surrogate for overall energy consumption (Xiufan and Decheng, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Therefore, this study uses the electricity consumption per 10,000 yuan as an indicator to reflect the impact of energy factors on carbon intensity. In China, power generation is predominantly thermal-based, which is heavily reliant on coal and fossil fuels (Zhang, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Hence, this indicator is a positive one. The technological innovation factor is indicated by the number of patent grants and the proportion of scientific and educational expenditures in the total fiscal expenditure. Research and development investment affects technological change, and according to relevant studies, technological change is currently a positive indicator of carbon intensity in China (Shi, L. et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIndicator system affecting carbon intensity\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAffecting Factors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIndicators\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAbbreviation\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIndicators\u0026rsquo; Attribute\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eEconomic factors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePer capita GDP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePGDP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSecondary industry in GDP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSIP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDemographic factors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePermanent population\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUrbanization rate\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy factors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eElectricity consumption per 10,000 yuan\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTechnological innovation factors\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of patent grants\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePG\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eProportion of scientific and educational expenditures\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePSEE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e+\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: \u0026ldquo;+\u0026rdquo; indicates an increase in carbon intensity with an increase in the indicator value, while \u0026ldquo;\u0026minus;\u0026rdquo; indicates a decrease in carbon intensity with an increase in the indicators value.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Method\u003c/h2\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 Entropy method\u003c/h2\u003e \u003cp\u003eThe entropy method serves as an integrated indicator approach capable of consolidating multiple criteria that represent diverse allocation principles (Cui et al., 2020; He, D. et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Which determine weight indicators through the transmission of information quantity, calculate entropy values to reflect utility value, and thus obtain more reliable weights. Therefore, the entropy method is an objective approach to determining the degree of dispersion of each indicator, unaffected by the subjective influence of decision-makers (Wang et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The steps of the entropy method are as follows.\u003c/p\u003e \u003cp\u003eFirstly, the raw data need to be normalized. The normalized methods for positive indicators and negative indicators are respectively shown in formulas (1) and (2).\u003c/p\u003e \u003cp\u003ePositive indicator: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{ij}=\\frac{{x}_{ij}-{min}_{j}}{{max}_{j}-{min}_{j}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(1\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eNegative indicator: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{X}_{ij}=\\frac{{max}_{j}-{x}_{ij}}{{max}_{j}-{min}_{j}}\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e represents the normalized result of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e th indicator of city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e; \u003cem\u003ex\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e represents the original value of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e th indicator of city \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003e; \u003cem\u003emax\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e represents the maximum original value of the \u003cem\u003ej\u003c/em\u003e th indicator; \u003cem\u003emin\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e represents the minimum original value of the \u003cem\u003ei\u003c/em\u003e th indicator.\u003c/p\u003e \u003cp\u003eThe ratio of \u003cem\u003eX\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e to the sum of 332 cities of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\:\\)\u003c/span\u003e\u003c/span\u003eth indicator (\u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e) is calculated as follows:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:{P}_{ij}=\\frac{{X}_{ij}}{{\\sum\\:}_{i=1}^{n}{X}_{ij}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhen the differences in indicator values are greater, more useful information can be obtained from these differences, but the entropy value is smaller.\u003c/p\u003e \u003cp\u003eSecondly, based on the calculations, the weight calculation formulas for the seven indicators of the 332 studied cities are shown below.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{e}_{j}=\\frac{{\\sum\\:}_{i=1}^{n}{p}_{ij}\\text{ln}{p}_{ij}}{-\\text{ln}n}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere if \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e is 0, then \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003eln\u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e also is defined as 0.\u003c/p\u003e \u003cp\u003eThirdly, the weight of each indicator can be computed:\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{W}_{j}=\\frac{1-{e}_{j}}{{\\sum\\:}_{j=1}^{m}(1-{e}_{j})}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(5\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere the information entropy value of indicator \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e is represented by \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e, and \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e is the weight of the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:j\\)\u003c/span\u003e\u003c/span\u003e th indicator.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 IEPD method\u003c/h2\u003e \u003cp\u003eThe IEPD method focuses on \"average reduction\" and \"relative reduction\" during the distribution reduction process, including two variables: the average reduction rate and the relative reduction factor. The average reduction rate indicated the standard for proportional distribution, while the relative reduction factor served as a suitable adjustment following a set of fairness criteria. The CITRR in each city is calculated by the average reduction rate and the relative reduction factor (Shi, Longyu et al., 2020).\u003c/p\u003e \u003cp\u003eIn the IEPD method calculating process, the relative reduction factor \u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e needs to be determined based on the CITRR allocation indicator system, reflecting each city's differentiated emission reduction responsibilities based on proportional allocation. The calculation formula is as follows.\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{\\alpha\\:}_{i}=\\frac{\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}{\\frac{1}{n}\\sum\\:_{i=1}^{n}\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}\\left(n=1,\\dots\\:,332;m=1,\\dots\\:,7\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(6\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e represents the normalized value of the \u003cem\u003ej\u003c/em\u003e th indicator for the \u003cem\u003ei\u003c/em\u003e th city, \u003cem\u003eW\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e is the weight of the \u003cem\u003ej\u003c/em\u003e th indicator.\u003c/p\u003e \u003cp\u003eThe average CITRR of each city reflects the concept of equal distribution, which is calculated based on the overall target reduction rate \u003cem\u003eC\u003c/em\u003e required at the national level and the relative reduction factors of each city. The formula is as follows:\u003cdiv id=\"Equd\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equd\" name=\"EquationSource\"\u003e\n$$\\:\\stackrel{-}{x}=\\frac{C\\sum\\:_{i=1}^{n}{G}_{i}{I}_{i}}{\\sum\\:_{i=1}^{n}{G}_{i}{I}_{i}{\\alpha\\:}_{i}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(7\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{x}\\:\\)\u003c/span\u003e\u003c/span\u003eis the average CITRR for 332 cities. \u003cem\u003eI\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e represents the carbon intensity of city \u003cem\u003ei\u003c/em\u003e in 2020, and \u003cem\u003eGi\u003c/em\u003e represents the GDP of city \u003cem\u003ei\u003c/em\u003e in 2025.\u003c/p\u003e \u003cp\u003eFinally, the CITRR for city \u003cem\u003ei\u003c/em\u003e, namely \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{x}_{i},\\:\\)\u003c/span\u003e\u003c/span\u003eis given by the formula:\u003cdiv id=\"Eque\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Eque\" name=\"EquationSource\"\u003e\n$$\\:{x}_{i}=\\frac{C\\sum\\:_{i=1}^{n}{G}_{i}{I}_{i}}{\\sum\\:_{i=1}^{n}(\\frac{\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}{\\frac{1}{n}\\sum\\:_{i=1}^{n}\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}\\times\\:{G}_{i}{I}_{i})}\\times\\:\\frac{\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}{\\frac{1}{n}\\sum\\:_{i=1}^{n}\\sum\\:_{j=1}^{m}{Z}_{ij}\\times\\:{W}_{j}}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(8\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.3.3 K-means clustering method\u003c/h2\u003e \u003cp\u003eThe K-means clustering method is a classical clustering method with many applications. The results are presented in clusters, each containing a set of data points with similar characteristics. Such clustering outcomes are intuitive and easy to understand, facilitating interpretation and presentation. The clustering step of K-means consists of four steps (Li et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Moradi Fard et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2020\u003c/span\u003e):\u003c/p\u003e \u003cp\u003e(1) Using the elbow method or other methods to determine the optimal number of clusters (k). In this research, the elbow method result shows that the k is four after normalizing indicator values.\u003c/p\u003e \u003cp\u003e(2) Randomly selecting four data points as the initial cluster centers, calculating the distance from each data point to each cluster center, and assigning each data point to the cluster corresponding to the nearest cluster center.\u003c/p\u003e \u003cp\u003e(3) Recalculate each cluster's cluster centers, typically using the mean of all data points within the cluster as the new cluster center.\u003c/p\u003e \u003cp\u003e(4) Repeating the second and third steps until the cluster centers no longer change.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Data source and processing\u003c/h2\u003e \u003cp\u003eIn this study, the carbon intensity of cities is sourced from the \"China City CO\u003csub\u003e2\u003c/sub\u003e Emission Dataset\" (2020), whereas other socio-economic data are collected from the respective city statistical yearbooks (2021).\u003c/p\u003e \u003cp\u003eThis study employs the GM (1,1) model for GDP forecasting. Due to the large number of cities, when conducting the first round of GM (1,1) prediction from 2010\u0026ndash;2023, spanning 14 years, the prediction results of some cities were in the third and fourth-level grades. To improve the prediction results, the study selected these cities to carry out the second prediction round, and shortened the period to 2016\u0026ndash;2023, spanning 8 years. The results of the first prediction show that 254 cities achieved a first-level accuracy grade, 20 cities achieved a second-level accuracy grade, 17 cities achieved a third-level accuracy grade, and 41 cities achieved a fourth-level accuracy grade. Therefore, the second prediction selected 58 cities from the third and fourth-level accuracy grades for prediction. The prediction results show that 50 cities achieved a first-level accuracy grade, 4 cities achieved a second-level accuracy grade, and 4 cities achieved a third-level accuracy grade. GM (1,1) prediction accuracy grades are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGM (1,1) prediction accuracy grades\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eGrades\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAccuracy\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC\u003c/p\u003e \u003cp\u003e(Mean squared error ratio)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP\u003c/p\u003e \u003cp\u003e(Small error probability)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFirst-level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eGood\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC\u0026thinsp;\u0026le;\u0026thinsp;0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026ge;\u0026thinsp;0.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSecond-level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eQualified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.35\u0026lt;C\u0026thinsp;\u0026le;\u0026thinsp;0.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.80\u0026thinsp;\u0026le;\u0026thinsp;P\u0026lt;0.95\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThird-level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMarginally\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.50\u0026lt;C\u0026thinsp;\u0026le;\u0026thinsp;0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.70\u0026thinsp;\u0026le;\u0026thinsp;P\u0026lt;0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFourth-level\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUnqualified\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026gt;0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3 Results","content":"\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Indicators\u0026rsquo; weights\u003c/h2\u003e \u003cp\u003eThe objective weights of each indicator were calculated according to formula (5), as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. It can be seen that the weight of the EC indicator was the largest, W\u003csub\u003eEC\u003c/sub\u003e=0.407, indicating that in the allocation of carbon intensity, the differences in electricity consumption per 10,000 yuan were given the highest priority. PG factor followed, W\u003csub\u003ePG\u003c/sub\u003e=0.382. As calculated, the PP factor's weight was close to only a quarter of the EC factor. It ranked as the third highest among the seven types of factors (0.107). The weight values of the remaining four factors were all below 0.1, among which the PSEE factor has the lowest weight value, W\u003csub\u003ePSEE\u003c/sub\u003e=0.011, indicating that in the allocation of carbon intensity, the differences in the proportion of science and education expenditure to total fiscal expenditure were considered less important. The weight of the SIP factor is close to that of the PSEE, at 0.015. The weight values for UR and PGDP were 0.024 and 0.055, respectively.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eThe weights of the seven indicators\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFactors\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePDGP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSIP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eUR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eEC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003ePG\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003ePSEE\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWeight\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.055\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.107\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.024\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.407\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.011\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.2 CITRR results\u003c/h2\u003e \u003cp\u003eUnder the target constraint set by China's \"14th Five-Year Plan\" to achieve an 18% reduction in carbon intensity by 2025 compared to 2020, calculations based on formula 7 yield an average CITRR of 13.13%. Furthermore, considering the weight of the seven influencing factors, the CITRR assigned to individual cities exhibits notable variations, ranging from 2.76\u0026ndash;88.58%.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows cities with low CITRR located in China's border areas (the three northeastern provinces, Xinjiang, Tibet, and Yunnan) and cities with high CITRR distributed along the coastal cities. The target reduction rate for central cities tends to be at an intermediate level. By calculating the spatial autocorrelation of the CITRR, the Global Moran I correlation index is 0.24, with a p-value equal to 0, proving that the distribution of CITRR among the 332 cities exhibits spatial effects.\u003c/p\u003e \u003cp\u003eSpecifically, Shenzhen topped the list with a CITRR of 88.58%. Yushu Tibetan Autonomous Prefecture, Shanghai, Guangzhou, and Beijing followed closely behind, with CITRR of 78.99%, 72.44%, 67.84%, and 66.85%, respectively. This result was closely related to Shenzhen, Shanghai, Guangzhou, and Beijing's status as one of China's economic special zones, with a high level of economic development, the highest urbanization rate, and the largest number of patent authorizations among all cities, thus bearing the greatest task of carbon intensity reduction. However, the reasons for Yushu Tibetan Autonomous Prefecture's second-highest ranking in CITRR are unclear. In contrast, the Daxing'anling region had the lowest CITRR, at only 2.76%. The cities ranking second to fifth from the bottom in terms of CITRR were Yichun, Hegang, Qitaihe, and Jixi, with 4.02%, 4.99%, 5.07%, and 5.24%. It was noteworthy that all of the aforementioned five cities are located in Heilongjiang Province, and this aligns with its ecologically sensitive function as one of China's key state-owned forest areas and primary distribution areas for natural forests. The region had an average level of economic development, and its electricity consumption per 10,000 yuan, which carries the greatest weight, was the smallest among all cities. Hence, its CITRR was the lowest.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.3 CITRR results in different types of cities\u003c/h2\u003e \u003cp\u003eK-means clustering was applied to divide the 332 cities into four clusters, and the spatial distribution of the four clusters of cities is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eCluster 1 includes 77 cities, such as Harbin, Haikou, and Sanya, as well as some autonomous cities of ethnic minorities. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.152, SIP: 0.544, PP: 0.134, UR: 0.476, PG: 0.018, PSEE: 0.635, EC: 0.007 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The Liangshan Yi Autonomous Prefecture is the area closest to the cluster center among these cities. Cluster 1 cities\u0026rsquo; specific characteristics are that the secondary industry in GDP is relatively low, and the proportion of scientific and educational expenditures is also low in the four types of clustered cities. However, the electricity consumption per 10,000 yuan is the highest.\u003c/p\u003e \u003cp\u003eCluster 2 includes 117 cities, such as Shijiazhuang, Handan, Huanggang, and others. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.131, SIP: 0.36, PP: 0.056, UR: 0.513, PG: 0.005, PSEE: 0.425, EC: 0.027. The Kashgar region is the area closest to the cluster center among these cities. Compared to the other three types of cities, it has the second-highest permanent population and the second-highest proportion of scientific and educational expenditures.\u003c/p\u003e \u003cp\u003eCluster 3 includes 111 cities, such as Changchun, Taiyuan, Yantai. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.527, SIP: 0.57, PP: 0.379, UR: 0.817, PG: 0.334, PSEE: 0.716, EC: 0.003. Yancheng is the closest to the cluster center. This type of city's characteristic is that its per capita GDP is higher than cluster 1 and cluster 2 but slightly lower than cluster 4. Its secondary industry in GDP is the highest among the four types of cities.\u003c/p\u003e \u003cp\u003eCluster 4 includes 27 cities, such as Beijing, Shanghai, and Wuhan. The normalized values for the corresponding seven indicators are as follows: PGDP: 0.316, SIP: 0.678, PP: 0.1, UR: 0.663, PG: 0.036, PSEE: 0.57, EC: 0.009. Guangzhou is the city closest to the cluster center. The characteristic of this type of city is a higher proportion of scientific and educational expenditures. However, it has the lowest electricity consumption per 10,000 yuan among the four categories of cities.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe Kruskal-Wallis test, the P\u0026thinsp;\u0026lt;\u0026thinsp;0.001, indicates a significant difference in the CITRR among the four categories of cities. The range of CITRR for cluster 1 is 2.76\u0026ndash;10.01%; for cluster 2, it is 6.84\u0026ndash;15.33%; for cluster 3, it is 7.23\u0026ndash;21.56%, for cluster 4, it is 18.56\u0026ndash;88.58% (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). As for the cities closest to the cluster centers in each cluster, the city with the lowest CITRR is Guangzhou, in cluster 4, with a CITRR of 11.39%. The CITRR for Yancheng in cluster 3 and Kashgar region in cluster 4 are very close, consistent with the overall distribution characteristics of CITRR for these two categories of cities, at 18.59% and 15.57%, respectively. In contrast, the city with the highest CITRR is Liangshan Yi Autonomous Prefecture in cluster 1, with a CITRR nearly twice that of Guangzhou, reaching 20.01%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4 Discussions","content":"\u003cp\u003eIn the process of allocating carbon intensity reduction targets, equity and efficiency are complementary (Pan et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Efficiency without equity can lead to certain regions bearing a disproportionate burden, potentially undermining social cohesion and political support for climate policies. Conversely, equity without efficiency may increase overall costs and slow progress toward emission reduction targets. To reconcile these two principles, this study uses the decline in carbon intensity as an observation indicator, constructs multiple influencing factors such as economic, demographic, energy, and technological innovation, employs the entropy method to obtain the weights of the indicators, and introduces an IEPD method to obtain the CITRR for various cities during the 14th Five-Year Plan period. This research shows that balancing equity and efficiency in allocating carbon intensity reduction targets is crucial. Scientific methods and models can optimize the allocation, ensuring the reasonable development of each region and the fair sharing of emission reduction responsibilities.\u003c/p\u003e \u003cp\u003eCarbon intensity exhibits a significant regional clustering trend (Pang et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Zhao et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This study further confirms that the CITRR also has spatial characteristics, meaning regions with higher CITRR tend to be adjacent to regions with similarly high reduction targets. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the CITRR in coastal developed areas is significantly higher than inland areas, gradually decreasing from the eastern to the central and western regions. The eastern region of China, especially the coastal areas, demonstrates a higher economic scale, growth rate, and industrial strength, making it China's most economically active and developed region. Regions with higher levels of economic development are more inclined to adopt advanced emission reduction technologies and management measures, thus forming a spatial clustering effect of high carbon reduction rates (Guo and Yu, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Therefore, when formulating and implementing carbon reduction policies, it is necessary to encourage all regions to jointly set carbon reduction targets and policies to promote governance collaboration while considering the differences between regions and adopting differentiated and targeted measures to achieve more effective carbon reduction goals.\u003c/p\u003e \u003cp\u003eThe limitation of this study lies in the insufficient consideration of the impact of policy factors on emission reduction tasks. Policy factors include but are not limited to, local government emission reduction policies, incentive measures, regulatory restrictions, and the adoption of new technologies, all of which can significantly affect the completion of urban emission reduction tasks. For instance, a city with stricter environmental regulations and incentive policies may more effectively promote the implementation of emission reduction measures, thereby taking on more responsibility in emission reduction tasks. Conversely, suppose a city lacks sufficient policy support, even if it has a more significant potential for emission reduction. In that case, it may struggle to achieve its expected emission reduction targets due to inadequate policy incentives. Therefore, to allocate emission reduction tasks more accurately, future research needs to consider policy factors and develop more scientifically sound and reasonable schemes, ensuring the tasks' fairness and effectiveness while promoting the enthusiasm and innovation of various cities in the emission reduction process.\u003c/p\u003e"},{"header":"5 Conclusions and recommendations","content":"\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Conclusions\u003c/h2\u003e \u003cp\u003eThe weights of seven indicators affecting carbon emissions intensity, calculated using the entropy Method, are ranked from highest to lowest: EC, PG, PP, PGDP, UR, SIP, and PSEE. The IEPD method is used to calculate the CITRR, and the results of 332 cities show that the city with the highest CITRR is Shenzhen. At the same time, the lowest is the Daxing'anling region. Geographically, high CITRR cities are distributed in coastal areas, while low CITRR mainly sites in border regions, primarily in Heilongjiang Province, Xinjiang, and the Tibet Autonomous Region.\u003c/p\u003e \u003cp\u003eFurthermore, according to the spatial autocorrelation regression analysis, the CITRR's Global Moran I correlation index is 0.24, which means that the CITRR of the 332 cities exhibits spatial effects. Finally, based on their indicators characteristics, the 332 cities are divided into four clusters by the K-means clustering method, and the differences in CITRR among each cluster of cities are significant.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Recommendations\u003c/h2\u003e \u003cp\u003eDue to the differences in characteristics among the four categories of cities, the CITRR varies across each category. This study provides policy recommendations for each category of city, respectively.\u003c/p\u003e \u003cp\u003eCluster 1 belongs to those with relatively low levels of economic development, which implies a weaker capacity in allocating carbon intensity. Consequently, the CITRR is significantly lower. These cities should enhance their level of industrialization and increase investment in scientific research to develop high-tech industries, thereby improving their economic growth model.\u003c/p\u003e \u003cp\u003eThe CITRR of cluster 2 and cluster 3 are relatively close, indicating their similar comprehensive capabilities in reducing carbon intensity. Cluster 2, building on its high proportions of permanent population and scientific and educational expenditures, should further optimize the population structure and allocation of scientific and educational resources to enhance the efficiency of such expenditures. Cluster 3, while maintaining the stable development of the secondary industry, should focus on developing the tertiary sector, including the service industry and high-tech industries, to increase the diversification of the economy.\u003c/p\u003e \u003cp\u003eCluster 4 represents the top tier of comprehensive development, encompassing the most advanced cities in the country, which have a high degree of economic development. Consequently, the CITRR is significantly higher. These cities can leverage their economic development advantages to promote carbon finance operations, such as carbon quota trading, investment and financing, as well as bank loans.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003eThis work was supported by the National Natural Science Foundation of China 42001210.\u003c/p\u003e\n\u003cp\u003eData availability statement\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe datasets used and/or analysed during the current study available from the corresponding author on reasonable request. Contact email:\u0026nbsp;[email protected]\u003c/p\u003e\n\u003cp\u003eCRediT authorship contribution statement\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFengmei Yang:\u0026nbsp;\u003c/strong\u003eWriting \u0026ndash; original draft, Resources, Methodology, Investigation.\u0026nbsp;\u003cstrong\u003eYin Ren:\u0026nbsp;\u003c/strong\u003eProject administration, Conceptualization. \u003cstrong\u003eShudi Zuo:\u0026nbsp;\u003c/strong\u003eFunding acquisition. \u003cstrong\u003eJiaheng Ju:\u003c/strong\u003e Formal analysis, Software, Data curation.\u0026nbsp;\u003cstrong\u003eMeng Yang:\u0026nbsp;\u003c/strong\u003eWriting \u0026ndash; review \u0026amp; editing.\u003c/p\u003e\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAo, Z., Fei, R., Jiang, H., Cui, L., Zhu, Y. 2023. \u0026ldquo;How can China achieve its goal of peaking carbon emissions at minimal cost? 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This paper introduces a comprehensive carbon intensity reduction allocation scheme based on the entropy method and an improved equal-proportion distribution method (IEPD method), which integrates fairness and efficiency. Firstly, an indicator system including economic, demographic, energy, and technological innovation aspects is established, and the entropy method is employed to determine the weights of these indicators. Secondly, using the IEPD method, the carbon intensity reduction target for China's 14th Five-Year Plan period (namely, an 18% reduction in carbon intensity by 2025 compared to 2020) is allocated to 332 cities. Thirdly, K-means clustering is utilized to categorize the cities according to seven indicators, and the characteristics of the carbon intensity target reduction rate (CITRR) of each group are analyzed. The results show that: (1) The average CITRR of 332 cities is 13.13%, and the CITRR ranges from 2.76\u0026ndash;88.58%. (2) The CITRR shows a step-like regional distribution difference that gradually decreases from the eastern region to the central and western regions, and the Global Moran I correlation index is 0.24, indicating a positive spatial correlation. (3) K-means clustering divides 332 cities into four categories, and the Kruskal-Wallis test shows a significant difference in the CITRR among the four categories of cities. The allocation plan proposed in this study can help cities assess their carbon intensity reduction capabilities and formulate effective policies.\u003c/p\u003e","manuscriptTitle":"Allocation of Carbon Intensity Target Reduction Rate for China's 332 Cities Based on Entropy Method and Improved Equal-Proportion Distribution Method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-04-10 14:27:50","doi":"10.21203/rs.3.rs-6166405/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-04-16T03:16:16+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"198662387367641134481973183794588468241","date":"2025-04-15T02:42:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-04-14T10:44:59+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"185752871580219609508236124525313538982","date":"2025-04-10T10:26:30+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-03-26T08:16:07+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-03-26T02:14:56+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-03-26T00:41:42+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-03-22T08:09:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-03-06T02:38:12+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8ad9eac8-4e43-43f2-838b-87560bc503ab","owner":[],"postedDate":"April 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":46439640,"name":"Earth and environmental sciences/Environmental social sciences"},{"id":46439641,"name":"Earth and environmental sciences/Environmental social sciences/Climate change impacts"},{"id":46439642,"name":"Earth and environmental sciences/Environmental social sciences/Climate change policy"}],"tags":[],"updatedAt":"2026-01-19T16:48:54+00:00","versionOfRecord":{"articleIdentity":"rs-6166405","link":"https://doi.org/10.1038/s41598-026-35781-2","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2026-01-14 16:30:20","publishedOnDateReadable":"January 14th, 2026"},"versionCreatedAt":"2025-04-10 14:27:50","video":"","vorDoi":"10.1038/s41598-026-35781-2","vorDoiUrl":"https://doi.org/10.1038/s41598-026-35781-2","workflowStages":[]},"version":"v1","identity":"rs-6166405","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6166405","identity":"rs-6166405","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}