Exploring the impact of urban vitality on carbon emission mechanisms using multi-source data

Abstract

Urbanization and low-carbon development are critical issues of global concern. As urbanization has reached its middle to late stages, cities face the dual pressures of development and environmental challenges. This study constructed a theoretical framework for urban vitality in six dimensions: social, economic, cultural, environmental, spatial, and perceptual. Using methods such as spatial syntax, entropy-weighted TOPSIS, deep learning models, and geographic detectors, we analysed the distribution characteristics of urban vitality in Yantai’s central area, explored how vitality-contributing factors influenced carbon emissions, and elucidated the association of urban vitality with carbon emissions. The results indicated that (1) urban vitality exhibited a multicentred distribution pattern of “low in the hinterland—high along the coast”; (2) significant differences existed in the impacts of various vitality dimensions on urban carbon emissions; (3) different urban vitality factors have varying levels of explanatory power regarding the spatial distribution of carbon emissions, with maximum building height exhibiting the strongest explanatory power, while the selection degree shows the weakest; and (4) the interactions between these factors typically demonstrate a two-factor enhancement, with the interaction between maximum building height and integration having the most significant effect on urban carbon emissions. This study innovatively integrates three-dimensional spatial and cultural perception perspectives, addressing the biases found in previous research that represented urban vitality from a singular viewpoint. It provides a more comprehensive framework and methodology for evaluating urban vitality, and the findings can offer recommendations for building low-carbon, high-vitality, and sustainable urban environments.

Introduction

With the ongoing urbanization, significant changes have occurred in the living spaces of human populations¹. In China, the growing complexity of urban forms and scales has led to various negative impacts and urban challenges². Furthermore, China’s extensive growth model has not only exacerbated the urban heat island effect but also contributed to an imbalance in the quality of urbanization^3,4. In some regions, economic growth is prioritized over development quality, resulting in a lack of essential vitality within cities. Urban vitality and carbon emissions have received increasing attention in urban development, with urban form playing a crucial role as an important intermediary connecting the two in urban planning and design. Faced with issues such as economic decline, shrinkage of urban scale, and environmental protection associated with urbanization, as well as the backdrop of low-carbon urban development^2,5,6,7, it is vital to enhance our understanding of urban vitality and examine its relationship with urban carbon emissions. This is crucial for creating vibrant and sustainable cities that fulfill the requirements of sustainable urban development.

In 1961, Jane Jacobs was the first to introduce the idea of “urban vitality” to the field of urban studies. She noted that the interaction between people and their corresponding living spaces generates diverse and rich community life, as well as vibrant living environments⁸. In both domestic and international literature, the current measurement of urban vitality is approached through two key methods. First, urban vitality is assessed using large-scale, high spatiotemporal accuracy geographic annotation data such as mobile phone signalling, GPS, social media check-ins, LBS locations, Baidu heatmaps, and restaurant reviews^9,10. Second, a multidimensional index system is constructed to comprehensively measure urban vitality. For example, Huang et al. proposed a conceptual framework based on the intensity of social activity, economic activity, and pedestrian density to evaluate urban vitality⁹. Similarly, Zeng et al. evaluated urban vitality on the basis of population density, spatial quality, accessibility, and diversity and compared the spatial characteristics of urban vitality in Chicago and Wuhan¹¹. Furthermore, He et al. developed an evaluation system of urban vitality focusing on social, economic, cultural, and environmental dimensions and analysed the correlation between urban vitality and carbon emissions¹². Overall, research on urban vitality has shifted from qualitative theoretical studies to quantitative methods and from coarse-grained to fine-grained data, adopting a more diverse and human-centred perspective.

Cities are intricate and expansive systems, and urban vitality signifies the potential for survival, expansion, and development within a city, a potential invigorated by a well-operating urban form¹³. Lan et al. suggested that the geometric characteristics of urban morphology, although seemingly straightforward, more profoundly represent complex socioeconomic phenomena. They further investigated the intrinsic patterns through which population influx and social infrastructure influence urban dynamics¹⁴. Wu et al. investigated the mechanisms by which the internal urban form influences neighbourhood vitality through a series of urban morphology indicators, including external transportation networks, circulation systems, land use composition, and accessibility¹⁰. A well-structured urban form serves as a vital source of urban vitality and plays a significant role in reducing carbon emissions^13,15. Adequate urban form not only acts as a wellspring of urban vitality but also plays a critical role in curbing urban carbon emissions^13,15. Research on carbon emissions presently focuses largely on national¹⁶, regional¹⁷, provincial¹⁸, and municipal¹⁹ emissions levels, with less emphasis on the driving mechanisms of carbon emissions within urban areas²⁰. Synthesizing the literature, it is evident that urban carbon emissions are closely linked to urban size, land development, traffic planning, architectural form, and infrastructure^21,22,23. Li et al. investigated the relationship between urban land use and carbon emissions, focusing on the impact of different scales, by assessing the coupling relationship at both the regional and local levels in Chongqing from 2000 to 2015²². Dong et al. conducted a life cycle assessment of public transportation systems in Shenzhen and other cities to analyse their carbon emissions, thereby evaluating the effectiveness of public transportation in energy conservation and emissions reduction²³. Furthermore, He et al. conducted a case study in Guangzhou, integrating correlation analysis and random forest modelling to explore the relationship between three-dimensional spatial structure and carbon emissions and unravel the scale effects influenced by the three-dimensional spatial structure²⁴. A substantial body of research indicates a close link between urban vitality and carbon emissions, with urban form playing a critical role. For instance, land serves as a fundamental carrier of urban activities. By optimizing land structure and improving land management²⁵, emissions can be effectively reduced. Moreover, well-organized, compact, and varied land use contributes positively to urban vitality. Road density, accessibility, and connectivity influence the urban travel environment, thereby altering the travel behaviours of urban residents and directly or indirectly affecting carbon emissions²⁶. Additionally, during the expansion phase of a city²⁷, a higher road network density can enhance urban vitality. In the face of the demands for urban renewal and low-carbon construction in the rapid phase of urbanization, how to reduce carbon emissions, improve the urban environment, and enhance urban vitality through urban form and spatial structure planning is an important task in the ongoing process of urbanization. While there are many relevant studies, few directly explore the specific relationship and impact mechanism between urban vitality and urban carbon emissions, and empirical research based on empirical case data still needs to be strengthened.

On the basis of the aforementioned theoretical and practical foundations, as well as existing research gaps, this study aims to directly construct a research mechanism for the impact of urban vitality on urban carbon emissions through the urban form as an intermediary factor. This research breaks away from the traditional analytical paradigm of “social-economic-cultural-environmental” thinking, innovatively integrating three-dimensional spatial factors with human perception elements to create a six-dimensional indicator framework for urban vitality that includes social, economic, environmental, cultural, spatial, and perceptual factors, providing a more comprehensive perspective for quantifying urban vitality. In this study, the central urban area of Yantai was selected as the research zone. Yantai is representative of similar cities in developing countries undergoing rapid urbanization and can offer research paradigms for the sustainable development of these cities. By accurately identifying the mechanisms of influence of various urban vitality indictors on urban carbon emissions, this research aims to assist policy-makers and urban planners in implementing precise strategies to promote sustainable urban development characterized by “low carbon emissions and high vitality”, contributing to the achievement of the United Nations Sustainable Development Goal (SDG) 11.

In summary, in this study, a six-dimensional framework is employed to measure urban vitality, multisource big data is integrated, and the entropy-weighted TOPSIS model is used to analyse the spatial distribution characteristics of urban vitality. Furthermore, the Optimal Parameter Geographic Detector (OPGD) method is used to explore the mechanism of impact of urban vitality factors on urban carbon emissions, revealing how the elements that foster urban vitality influence the distribution of carbon emissions. The aim of this study is to provide a basis for low-carbon and high-vitality sustainable development of Yantai and to offer developmental insights for urban planning in other regions.

Research area and dataset

Overview of the research area

Yantai is a central city on the Shandong Peninsula and a key port city under the “Belt and Road” initiative in the Bohai Rim region (36.40°N ~ 37°42′N; 120°50′E ~ 121°57′E). The city of Yantai is centered around the Zhifu coastal area and expands east and west while connecting the mountains and the sea to the north and south. The overall terrain is primarily characterized by low hills, and the land use types are diverse, presenting gentle undulations with distinct features. As of 2024, the installed capacity of clean energy in the city has reached 17.4151 million kilowatts, maintaining its leading position in the province. The districts of Zhifu and Fushan have been recognized among the top 100 districts in the country for high-quality development and green development, respectively. According to statistics, the proportion of days with good air quality in Yantai last year was 88.3%, and the annual average for fine particulate matter (PM2.5) was 25 µg per cubic meter, ranking second in the province. This study focuses on five districts in the central urban area of Yantai—Zhifu District, Fushan District, Laishan District, Penglai District, and Muping District (excluding island areas)—as the research subjects, covering an area of 4058.91 square kilometers (Fig. 1). The resident population is 2.5947 million, with the urban population accounting for 80.64%. The total Gross domestic product (GDP) in the research area is 543.574 billion yuan.

Fig. 1

Overview of the study area. Notes: Plotted by the author. The map was generated using ArcGIS 10.8(https://www.esri.com/en-us).

Research data

Basic geographic data

(1) Normalized Difference Vegetation Index (NDVI) and GDP data were obtained from the Resource and Environment Science Data Center (https://www.resdc.cn/data.aspx?DATAID=360). (2) The building data were obtained from CNBH-1029 (https://wwanben1994.users.earthengine.app/view/cnbh10mtest). This model uses multisource Earth observation data and machine learning techniques to comprehensively account for the effects of factors such as shadows on building height estimation using a multiwindow statistical approach. CNBH-10 m is the first 10-m resolution building height estimation model for China. The building vector data were sourced from the AutoNavi Map and Tianditu Data Platform and include information such as the building footprint area and number of stories. (3) Road data were obtained from OpenStreetMap (OSM) (https://www.openstreetmap.org/) and, in conjunction with remote sensing imagery, were employed to extract primary roads, secondary roads, minor roads, and highways for this study.

Points of interest (POI) data

The POI data were sourced from the Baidu Map Open Platform by accessing the API through Python scripts in 2023. The collected data cover 14 categories, including accommodations, shopping, catering, health care and social security, education and culture, sports and leisure, tourism attractions, real estate and parks, transportation, and life services, on the basis of the “Classification and Coding of Geographical Information Interest Points” (GB/T 35,648–2017) published by the National Standardization Administration of China. Each POI entry includes location coordinates (latitude and longitude), place name, address, phone number, and classification information. During data processing, the coordinates were converted to the WGS84 coordinate system²⁸. Following data cleaning and categorization, a total of 105,014 valid POI data entries were obtained.

Panoramic streetview images data

The street space, as an important component of urban space, acts as a platform for residents’ daily activities and movement. As big data and computer semantic segmentation technology continue to develop, more and more scholars are applying street view images to the study of public space issues, conducting analyses on aspects such as street landscapes and street vitality, and performing precise analyses of complex built environments. The Baidu Map Open Platform (https://lbsyun.baidu.com/) is a set of service interfaces specifically tailored for developers, based on Baidu Maps. It is compatible with various platforms and provides a range of services, including basic static maps, location queries, route planning, public transportation inquiries, and static panoramic images. In this study, 4,326 sampling points were generated on the basis of processed OSM road network data at 300-m intervals. The collection of street view data was performed according to the following standardized procedure: (1) Data acquisition: A Python script was developed to automate data collection by calling the Baidu Panoramic Static Map API (version 2.0), allowing for the batch acquisition of street view images using the geographic coordinates of the sampling points. The data collection took place in March 2024. (2) Parameter settings: For each sampling point, four street view images were collected from a 90° horizontal perspective (orientations of 0°, 90°, 180°, and 270°), with the vertical perspective uniformly set at 0°. (3) Image processing: Image stitching was performed using OpenCV to generate panoramic images of 2400 × 400 pixels, incorporating smooth transitions to ensure comprehensive coverage of the spatial features of the street environment.

The extraction of street view images involved the utilization of the SegNet algorithm, a deep learning-based fully convolutional neural network, for the identification of spatial features within the street environment. SegNet is specifically tailored for image semantic segmentation, thus enabling the semantic classification of individual pixels within an image, thereby allowing for the recognition of elements such as the sky, sidewalks, lanes, buildings, and greenery^29,30. The proportions of these elements within each street view image were subsequently computed. Upon completion of data cleaning, filtering, and the removal of invalid images, a final dataset comprising 2,855 identifiable and valid street view images was obtained (Fig. 2).

Fig. 2

Example of SegNet segmentation results.

ODIAC data

Carbon emission data originated primarily from the Open Data Inventory for Anthropogenic Carbon Dioxide (ODIAC), available at https://db.cger.nies.go.jp/dataset/ODIAC/, with a spatial resolution of 1 km × 1 km. This global high-resolution dataset of anthropogenic carbon emissions is estimated on the basis of fossil fuel consumption, supplemented by regional power plant data and satellite observations of nighttime light intensity³¹. The accuracy of the ODIAC carbon emissions data exceeds 80%, and this dataset has been widely applied in international research related to carbon emission modelling, simulation, and prediction^32,33. Processing the monthly average data from ODIAC for 2023 yielded a spatial distribution map of annual carbon emissions for Yantai, revealing a higher concentration in the central urban area with a decreasing trend radiating outwards. Remote sensing imagery and onsite investigations indicate that regions with significantly elevated values correspond to the locations of power plants (Fig. 3).

Fig. 3

Spatial distribution map of carbon emissions in Yantai city. Notes: Plotted by the author. The map was generated using ArcGIS 10.8 (https://www.esri.com/en-us).

Methods

Construction of the research approach and indicator system

Research approach

This study follows a systematic analytical process: First, a 1 km × 1 km grid system was created and overlaid onto the study area boundary, defining 6,686 research units. To eliminate the influence of incomplete grid cells due to the coastline on the analysis results, all subsequent analyses utilized indicators standardized by the actual land area of each grid to ensure the scientific validity and comparability of the results. Second, an urban vitality evaluation system was constructed from six dimensions: social, economic, cultural, environmental, spatial, and perceptual. Based on foundational data processing using models such as Hill numbers and spatial syntax, and considering the diversity of indicator types, the study utilized an entropy-weighted TOPSIS method to standardize each indicator (fixing the value range between 0 and 1) and to comprehensively measure the level of urban vitality. Finally, based on these measurements, a systematic exploration of the overall spatial distribution characteristics of urban vitality in the central urban area of Yantai City was conducted, analyzing the relationship between vitality across various dimensions and the spatial distribution of carbon emissions. Finally, an OPGD was employed to quantitatively reveal the degree to which different urban vitality construction elements influence the spatial differentiation characteristics of carbon emissions.

Construction of the indicator system

The evaluation of urban vitality is a comprehensive assessment process that involves multiple layers, systems, and dimensions. Although its current definitions are overly broad and lack a unified understanding, different disciplines offer diverse interpretations. Recent research trends indicate a growing consensus in academia that “urban vitality is essentially a social and spatial composite, reflecting nonmaterial activities influenced by urban form and the built environment” (Ye Yu, Marcus, 2010; Lees, 2010; Oliveira, 2013). For example, Ye et al. conducted an analysis of street vitality with a focus on functional mix and the human perception of street morphology. In contrast, Long Ying et al. studied 286 cities in China with a minimum research unit of 1 km and employed regression models to reveal the impact of urban form indicators (e.g., road network density and land use diversity) on urban economic vitality, finding that all form indicators were significantly correlated with urban economic vitality.

Therefore, this study builds on the aforementioned research framework and existing studies, aiming to quantify urban vitality using urban morphological elements and multisource data that represent human activities to construct an evaluation index system for urban vitality in the central urban area of Yantai³⁴ (Table 1). Social vitality reflects the aggregation and activities of people. Factors such as density, small blocks, old buildings, accessibility, and diversity trigger crowd aggregation, which in turn stimulates urban vitality in the area. Considering the balance of indicators and data availability, this study selects functional mix (including disorder, richness and aggregation) and road accessibility (including choice, connectivity and integration) as measures of social vitality^8,35. Economic vitality serves as the driving force of urban vitality, representing the combination of the microlevel metabolism of urban economic entities and macrolevel high-growth states. The selected indicators for measuring economic vitality include the density of dining facility and per capita GDP (GDPpc), both of which significantly impact regional economic levels³⁶. Cultural facilities and participation in cultural activities notably influence the quality of urban life. Thus, this study employs the cultural facilities density as an indicator of cultural vitality. Environmental vitality is a crucial factor influencing the socioeconomic characteristics and cultural atmosphere of a region³⁷. Furthermore, urban green spaces play a significant role in shaping residents’ health and enhancing the quality of their living environments. This research uses the NDVI³⁸ to characterize environmental vitality. Spatial vitality represents a critical quality of urban vitality and is informed by architectural characteristics. This study integrates both two- and three-dimensional perspectives, selecting indicators such as the floor area ratio (FAR), building coverage ratio (BCR), average building height (ABH), and maximum building height (MBH) to comprehensively characterize urban spatial vitality. Finally, perceptual vitality captures the subjective experiences of residents. By examining the objective physical environment through physiological and psychological dimensions, this research underscores the importance of fostering enthusiasm among individuals to create urban vitality and expands upon the index system, which has relied predominantly on objective variables in previous studies. In this research, the green view index (GVI), sky view factor (SVF) and sidewalk ratio are employed as indicators of perceptual vitality.

Table 1 Indicator system for urban vitality assessment.

Entropy-weighted TOPSIS

The entropy-weighted TOPSIS method constitutes a sophisticated multicriteria decision-making framework that integrates the entropy weighting technique with the TOPSIS approach³⁹. The entropy weighting method enables the standardization of raw data, the computation of entropy values for each indicator, and the assignment of corresponding weights. The TOPSIS method subsequently determines the optimal and worst values, as well as the proximity of each evaluation object, thereby enabling a systematic ranking of the evaluation objects on the basis of the final scores⁴⁰. Currently, the TOPSIS method has been widely applied in evaluative research pertaining to the high-quality development of new urbanization, urban planning, and other fields⁴¹. Accordingly, this study adopts the entropy-weighted TOPSIS model as a comprehensive evaluative framework for urban vitality, aiming to provide more precise and objective weight allocations⁴².

Spatial autocorrelation analysis

To explore the spatial correlations among multiple variables, Anselin et al. proposed bivariate spatial autocorrelation theory, building on univariate spatial autocorrelation. This method quantitatively analyzes the correlation characteristics of various geographic factors in spatial distribution, effectively revealing their spatial relationships⁴³. To investigate the correlations and differences between urban vitality across different dimensions and the spatial distribution of urban carbon emissions, this study employs local spatial autocorrelation analysis⁴⁴ and uses GeoDa software to create Local Indicators of Spatial Association (LISA) cluster maps for a visual representation of the spatial correlation between the two. The specific formula for bivariate local spatial autocorrelation is as follows:

$${\text{I}}_{{{\text{ab}}}}^{\prime } = \frac{{{\text{x}}_{{\text{a}}}^{{\text{i}}} - \overline{x}_{{\text{a}}} }}{{\sigma_{{\text{a}}} }} \times \sum\limits_{{{\text{j}} = 1}}^{{\text{n}}} {{\text{W}}_{{{\text{ij}}}} \frac{{{\text{x}}_{{\text{b}}}^{{\text{j}}} - \overline{x}_{{\text{b}}} }}{{\sigma_{{\text{b}}} }}}$$

where ${\text{x}}_{\text{a}}^{\text{i}}$ represents the value of attribute a located in cell i; Where ${\text{x}}_{\text{b}}^{\text{j}}$ represents the value of attribute a located in cell j; $\overline{x}_{{\text{a}}}$ and $\overline{x}_{{\text{b}}}$ denote the respective average values of attributes a and b; $\sigma_{{\text{a}}}$ and $\sigma_{{\text{b}}}$ correspond to the variances of attributes a and b; and ${\text{W}}_{\text{ij}}$ stands for the weight coefficient matrix. Given that any two spatial units in this study share edges and vertices, the phenomena under investigation can produce spatial spillover effects through direct interactions across administrative boundaries or vertex contacts. Therefore, this study employs a first-order Queen contiguity matrix (rank = 1) for constructing the spatial weight matrix. In this methodology, the weight is assigned a value of 1 when two spatial units share a boundary or vertex, and 0 otherwise. Additionally, the Queen contiguity matrix captures small-scale spatial dependence more comprehensively than the Rook contiguity matrix, facilitating a more thorough investigation of spatial correlations⁴⁵.

Spearman correlation analysis

The Spearman correlation coefficient is a non-parametric statistical method that assesses the monotonic relationship (including but not limited to linear relationships) between two variables based on the ranks of the variables (i.e., the ordinal values assigned after sorting the variable values). Its range is from − 1 to 1, where a larger absolute value indicates a stronger correlation. This method does not require the data to meet normal distribution or linearity assumptions and is insensitive to outliers, making it suitable for analyzing non-linear but monotonic relationships.

In this study, the six dimensions of urban vitality (social, economic, cultural, environmental, perceptual, and spatial) and the comprehensive vitality index were transformed into spatial unit variables using grid-based value assignment, alongside carbon emissions data. Since these variables may exhibit non-normal distributions, contain local outliers, or demonstrate complex non-linear associations with carbon emissions, employing the Spearman correlation coefficient provides a more reliable method for analyzing their relationships. The specific analysis was conducted using SPSS 27.0: first, the grid-assigned vitality values for each dimension and the carbon emissions data were imported into SPSS; second, a bivariate correlation analysis was performed (Analyze > Correlate > Bivariate) with the Spearman option selected; finally, the correlation coefficient matrix and significance test results were obtained from the output.

Optimal parameter geodetector model

Geodetector is a spatial statistical model used to detect spatial heterogeneity and assess the relationships between influencing factors and other geographic variables. Its main advantage is that it is unaffected by multicollinearity, thereby avoiding endogeneity issues between independent and dependent variables⁴⁶. The optimal parameter geodetector model enhances the original geodetector model by selecting the best discretization algorithms and parameters, thus improving the model’s accuracy and interpretability in practical applications. This study implemented the OPGD model using the “GD” package in R. The model systematically evaluated four discretization methods for the continuous driving factors: equal intervals, natural breaks (Jenks method), quantile method, and geometric interval method, which are suitable for categorization into 3–10 classes. Based on the geodetector algorithm, OPGD automatically selects the optimal discretization parameters (methods and number of intervals) for each driving factor by comparing the results of the q statistic⁴⁷.

• (1) Factor Detector

  Factor detection is used to measure the degree of spatial heterogeneity in the explanatory power of a factor X for an attribute Y, as represented by the q statistic. In this study, the factor detector is employed to investigate the explanatory power of the factors that contribute to urban vitality with respect to carbon emissions. The specific formula is as follows:

$${\text{q = 1}} - \frac{{\sum\nolimits_{{\text{h = 1}}}^{{\text{L}}} {{\text{N}}_{{\text{h}}} \sigma_{{\text{h}}}^{{2}} } }}{{{\text{N}}\sigma^{{2}} }}{ = 1} - \frac{{{\text{SSW}}}}{{{\text{SST}}}}$$

In the equation, q represents the explanatory power, with a range of [0, 1]. The variable h represents stratification, while ${\text{N}}_{\text{h}}$ and N denote the number of units in stratification h and in the entire region, respectively. Additionally, $\sigma_{{\text{h}}}^{{2}}$ and $\sigma^{2}$ represent the variances of carbon emissions Y, corresponding to stratification h and to the entire region, respectively. SSW and SST refer to the within-group sum of squares and the total sum of squares, respectively.

• (2) Interaction Detection

  Interaction detection is used to examine the interactions among different independent variables. In this study, interaction detection was employed to investigate the enhancing or diminishing effects of the interactions among factors that contribute to urban vitality on carbon emissions, as well as the independent relationships among these different factors. The results of the interactions between two factors can be classified into five categories (Table 2).

Table 2 Detection of interactions.

• (3) Ecological Detector

  The ecological detector is specifically designed to compare whether there are significant differences in the spatial distribution of attribute Y influenced by the two factors, X1 and X2. It measures this using the F statistic:

$$F = \frac{{N_{X1} \left( {N_{X2} - 1} \right)SSW_{X1} }}{{N_{X2} \left( {N_{X1} - 1} \right)SSW_{X2} }}$$

$$SSW_{X1} = \sum\limits_{h = 1}^{L1} {N_{h} \sigma_{h}^{2} }$$

$$SSW_{X2} = \sum\limits_{h = 1}^{L2} {N_{h} \sigma_{h}^{2} }$$

In the formula: N_X1 and N_X2 represent the sample sizes of the two factors X1 and X2, respectively; SSW_X1 and SSW_X2 represent the sums of the intra-group variances formed by X1 and X2, respectively; L1 and L2 denote the number of layers for variables X1 and X2, respectively. The null hypothesis H0 states that SSW_X1 = SSW_X2. If H0 is rejected at the significance levelα, this indicates that there is a significant difference in the effects of the two factors X1 and X2 on the spatial distribution of attribute Y.

Results

Spatial patterns and correlations of urban vitality distribution

As shown in Fig. 4A, the central urban area of Yantai displays a ‘central low-coastal high’ ‘polycentric’ spatial differentiation pattern in terms of urban vitality, further characterized by a discernible “central-peripheral” gradient, indicating a gradual decline in spatial distribution. The northern coastal development belt has created a contiguous area that constitutes a high-value aggregate zone, demonstrating a “multipolar” urban vitality “ridge” led by the construction areas of Zhifu, Lai Shan, Fu Shan, Muping, and Penglai. In contrast, the southern region presents a “lower-intensity” zone of urban vitality. From an overall spatial perspective, high-vitality regions are predominantly concentrated in economically developed urban construction areas, whereas low-vitality regions are primarily clustered in the peripheral areas to the northwest and southwest. From the standpoint of functional clustering, areas exhibiting high comprehensive urban vitality are situated primarily around commercial centres, residential neighbourhoods, and educational institutions. This partially supports the validity of the evaluation outcomes presented in this study.

Fig. 4

Spatial distribution of multi-dimensional vitality in the central urban area of Yantai. (A). Comprehensive Vitality; (B). Social Vitality; (C). Economic Vitality; (D). Cultural Vitality; (E). Environmental Vitality; (F). Spatial Vitality; (G). Perceived vitality). Notes: Plotted by the author. The map was generated using ArcGIS 10.8 (https://www.esri.com/en-us).

The multidimensional analysis of urban vitality depicted in Fig. 4B–G reveals that the social, economic, cultural, spatial, and perceptual vitality in the central urban area of Yantai exhibit a spatial structure similar to that of comprehensive urban vitality. High-value areas for urban vitality across these dimensions are predominantly located in Zhifu District, with secondary high-value centres in Muping District and Penglai District, showing a general decreasing trend from the northern coastal belt towards the south. The main reason is that the central urban area of Yantai features a typical multiclustered, multicore, linear coastal city structure, with socioeconomic resources largely concentrated in urban construction areas. In contrast, the trend in the spatial distribution of environmental vitality is reversed; owing to the prevalence of mountainous green spaces and surface water systems in the southern region, environmental vitality is greater in the southern areas and lower in the northern coastal belt. In terms of spatial equity, social vitality has the most balanced spatial distribution among the various dimensions, with spatial vitality coming next and cultural vitality demonstrating the least balanced distribution.

Relationship between multidimensional vitality and spatial distribution characteristics of carbon emissions

Using Spearman correlation analysis, we further assessed the relationships in spatial distribution between carbon emissions and various forms of vitality, including comprehensive vitality, social vitality, economic vitality, environmental vitality, cultural vitality, spatial vitality, and perceptual vitality, as shown in Table 3. Carbon emissions and urban spatial vitality have the highest correlation coefficient (r = 0.639), followed by comprehensive vitality (r = 0.580), social vitality (r = 0.526), economic vitality (r = 0.526), perceptual vitality (r = 0.480), and cultural vitality (r = 0.400), with a negative correlation identified for environmental vitality (r =  − 0.475). Excluding environmental vitality, the correlation coefficients relating carbon emissions to the various dimensions of urban vitality all significantly exceed 0, indicating a positive spatial association linking urban vitality to carbon emissions. The correlations between urban carbon emissions and the various dimensions of urban vitality differ significantly, indicating that urban vitality is not solely determined by a single factor. Additionally, the different dimensions and factors of vitality exert varying influences on carbon emissions. The spatial distribution of urban carbon emissions is most closely aligned with the distribution of spatial vitality, corroborating the findings presented in Fig. 6, where spatial vitality factors contribute significantly more to carbon emissions than other elements of vitality.

Table 3 Correlation coefficients between carbon emissions and urban vitality in different dimensions.

Through a comprehensive comparison of the spatial distribution and differentiation features of carbon emissions and urban vitality across various dimensions, the cluster analysis results (refer to Fig. 5A–G) indicate that comprehensive, social, economic, cultural, spatial, and perceptual vitality all exhibit an H–H agglomeration trend with carbon emissions in the central urban area, while demonstrating an L-L agglomeration spatial relationship in the southwestern region (Fig. 5A, B, C, D, F, G). Conversely, economic, cultural, and perceptional vitality all exhibit a L–H agglomeration at the edge of the central area in relation to carbon emissions (Fig. 5B, C, G). This is primarily due to the presence of numerous residential communities in this area, coupled with limited consumption venues and functional agglomerations, resulting in a relatively high proportion of single residential functions. High population and building densities contribute to comparatively high carbon emissions, whereas the absence of economic activities results in lower levels of economic, cultural, and perceptual vitality. The distributions of environmental vitality and carbon emissions show an L–H agglomeration trend within built-up areas and peripheral areas (Fig. 5E). This can be attributed to the central urban area being a built-up area with high population density, whereas the peripheral areas are situated farther from the built-up area and feature sparse populations and dense mountainous forests. Moreover, higher NDVI indices indicate a stronger carbon absorption capacity. The analysis reveals an H–H agglomeration of spatial vitality and urban carbon emissions in the central urban area (Fig. 5F), with clusters of L-L agglomeration in a scattered distribution in the surrounding areas. This is due to the high population density and proximity to the city centre, as well as the extensive vegetation coverage despite the closeness to the city centre.

Fig. 5

Cluster analysis of spatial distribution of multidimensional urban vitality and carbon emissions in the central urban area of Yantai city ((A). Comprehensive Vitality and Carbon Emissions; (B). Social Vitality and Carbon Emissions; (C). Economic Vitality and Carbon Emissions; (D). Cultural Vitality and Carbon Emissions; (E). Environmental Vitality and Carbon Emissions; (F). Spatial Vitality and Carbon Emissions; (G). Perceptual Vitality and Carbon Emissions). Notes: Plotted by the author. The map was generated using GeoDa 1.20 (https://geodacenter.github.io).

Detection of influencing factors on the spatial characteristics of carbon emissions based on OPGD

The results of the factor detection based on the OPGD systematically reveal the mechanisms by which various urban vitality indicators influence the spatial distribution of carbon emissions (Fig. 6). All factors passed the significance test at the 1% level (p < 0.01), indicating that each indicator has a statistically significant effect on the spatial differentiation of carbon emissions. In terms of explanatory power, the q-values of the factors range from 0.0704 to 0.7299, displaying a clear gradient difference. Notably, MBH has the most pronounced explanatory power (q = 0.7299), underscoring the dominant role of building morphology in the carbon emission pattern. The integration (q = 0.5495), ABH (q = 0.5472), and FAR (q = 0.5377) constitute a strong hierarchy of explanatory power, further confirming the key role of spatial morphological elements. The q-values of eight additional indicators, including density of dining facilities, GDPpc, and density of cultural facilities, fall between 0.3624 and 0.4710, indicating a moderately high explanatory power.

Fig. 6

Contribution of urban vitality factors to urban carbon emissions (q-statistic). Notes: The relative magnitudes of the q-statistics for each factor are shown. The contribution of all factors is significant at the p < 0.001 level (***).

The interaction detection analysis further reveals the complex synergy mechanisms among the driving factors (Fig. 7). The results show a general interactive enhancement effect of urban vitality indicators on carbon emissions, predominantly characterized by two-factor enhancement, although there are exceptions. The analysis of interaction types indicates that the synergistic effects between factors are largely dominated by “two-factor enhancement,” which means that for the majority of factor pairs, their explanatory power for carbon emissions demonstrates a linear superposition. Additionally, a unique “non-linear enhancement” effect exists between choice and NDVI, suggesting that their synergy goes beyond simple linear addition. Conversely, the interaction between richness and aggregation exhibits a “weakening” characteristic, as their interactive explanatory power does not exceed the independent explanatory power of either factor, implying potential overlap or cancellation in their underlying mechanisms affecting carbon emissions. In terms of interaction intensity, the integration and MBH exhibit the strongest interaction (qv12 = 0.8131). Other combinations with significant explanatory power include MBH with the density of dining facilities (qv12 = 0.7587) and MBH with NDVI (qv12 = 0.7584). This indicates that the interplay among road network structure, building morphology, commercial activities, and natural elements collectively shapes the spatial pattern of carbon emissions. It illustrates that the spatial differentiation of urban carbon emissions is driven by the synergy of multidimensional vitality elements, which encompasses both widespread two-factor enhancement effects and localized non-linear interaction mechanisms. The findings suggest that future urban carbon reduction strategies should prioritize the collaborative effects among factors, promoting cross-dimensional and systematic governance pathways to more effectively guide low-carbon urban development.

Fig. 7

Detection of interaction effects among influencing factors of urban carbon emissions.

The results of the ecological detectors indicate that the impact mechanisms of urban vitality factors on the spatial distribution of carbon emissions exhibit considerable heterogeneity (Fig. 8). Among all factor combinations, the vast majority show statistically significant differences (p < 0.05), confirming that multidimensional urban vitality elements exert relatively independent pathways in driving carbon emissions. However, the study also identifies several factor pairs that do not show significant differences, primarily concentrated in two categories: one involves internal indicators of functional mix, such as disorder, richness, and aggregation; the other pertains to certain spatial morphology and environmental perception indicators, such as integration with FAR, ABH; and NDVI with BCR, GVI, and SVF. This suggests that the aforementioned factors may share similar explanatory dimensions or mechanisms when influencing the spatial differentiation of carbon emissions. Therefore, in the context of urban low-carbon governance, targeted regulatory strategies should be implemented for factors with significant differences in their driving effects, while collaborative and integrated management measures may be considered for those with similar influences. This approach will help optimize policy resource allocation and enhance governance efficiency.

Fig. 8

Ecological detection of the driving effects of urban vitality factors on urban carbon emissions. Notes: Y represents a significantdifference, N means a no significant difference.

Discussion

Analysis of urban vitality spatial patterns

Based on the research results regarding the assessment of urban vitality in the central urban area of Yantai and its mechanisms impacting carbon emissions, this study explores pathways to enhance the construction of high-vitality, low-carbon cities in the context of “urban renewal” and “dual carbon” goals, following the principles of prioritizing ecological construction, enhancing spatial quality, focusing on key areas, and implementing localized policies (Fig. 9). As a mediating factor between urban vitality and carbon emissions, urban morphology can enhance urban vitality by optimizing the city layout in dimensions such as social, economic, cultural, environmental, spatial, and perceptual aspects. Additionally, a reasonable structure and urban planning can help reduce carbon emissions and increase carbon sinks.

Fig. 9

Diagram of the enhancement path for low-carbon and high-vitality urban development.

Among them, the results of the multidimensional vitality distribution indicate that the overall urban vitality in the central urban area of Yantai exhibits a decreasing distribution pattern from the center to the periphery. This resonates with the concentric circle model and central place theory found in classical urban spatial structure theories, confirming the cross-regional applicability of the radiation effect that high-vitality areas have on their surrounding zones. The areas with high vitality values in the study region are predominantly located in the northern coastal built-up area, which aligns with the findings of Fu Zhigang and others, indicating that high-vitality regions in Asia are often concentrated in the built-up areas of city centers⁴⁸. Unlike inland cities, Yantai, as a coastal city, is located relatively close to the sea, and the economic development of the coastal areas has driven the enhancement of urban vitality. Consequently, the study area exhibits an urban morphology featuring a pattern of “low vitality in the hinterland—high vitality along the coast. Furthermore, Yantai’s urban vitality demonstrates an increasingly evident spatial differentiation towards a “multi-centered” model, with the Zhifu, Fushan, and Laishan built-up areas depicting the highest urban vitality, followed by Muping and Penglai. This indicates the urban development process and the degree of population concentration. In areas with high vitality, there are generally taller buildings, increased BCR, and well-developed transportation infrastructure, highlighting the critical role of three-dimensional space and the social environment in urban vitality. This includes factors such as population mobility, social activities, economic development, and urban construction, all of which are pivotal in influencing urban vitality. Future efforts to enhance urban vitality across different areas could focus on improving infrastructure layout, diversifying commercial formats, and creating a conducive consumer environment as part of urban sustainable development endeavors.

Examining the vitality values across various dimensions, these dimensions are clearly interrelated and mutually impact each other (Supplementary Fig. 1, Supplementary Table 1), with all being intrinsically connected to population clustering activities. Establishing the capacity to gather people in urban areas expands the reach of social vitality, fosters economic activities, and makes spatial patterns more pronounced. In contrast, regions with high economic vitality typically exhibit elevated levels of social vitality; however, areas with high social vitality can simultaneously display both high and low economic vitality. This finding aligns with the research conducted of Yang, Li, and others, which suggests that social vitality is distributed more uniformly and extensively than economic vitality^12,49. Chen et al. compared community vitality with pedestrian flow on street maps to explore the fundamental drivers of urban vitality⁵⁰. Consistent with the results of this study, Chen’s research also demonstrated the positive impact of commercial activities on urban vitality. Similarly, areas characterized by high cultural and perceptual vitality tend to cluster in regions with elevated levels of economic and social vitality. This finding corresponds with Liu et al.’s results, indicating that enhancing cultural and recreational activities can indirectly stimulate the growth of urban vitality⁵¹. Environmental vitality is negatively correlated with other dimensions of vitality and is influenced by the natural features of Yantai. As a mountainous and coastal city, Yantai’s urban development relies on its natural environmental foundation, as mountainous areas with high environmental vitality have high green space coverage while exhibiting lower vitality across other dimensions. Therefore, the enhancement of urban vitality should not rely on a single dimension; it should instead involve systematic planning to promote the coordinated development of multiple dimensions of vitality.

Finally, by comparing urban vitality represented by big data such as nighttime light and mobile signaling data, we find that urban vitality measured using the six-dimensional indicator system of ‘social, economic, cultural, environmental, spatial, and perceptual’ is closely aligned with the vitality captured by multi-source big data⁵². This suggests that the urban vitality indicator system developed in this study is feasible. Moreover, the urban vitality constructed from these indicators has been reasonably weighted using the entropy-weight TOPSIS method, allowing for a more in-depth analysis of the spatial distribution characteristics and patterns of both comprehensive and dimension-specific urban vitality. This provides a more detailed basis for policy guidance and theoretical exploration.

Analysis of the relationship between urban vitality and carbon emissions

The core leadership of spatial vitality and the driving role of architectural form

Spatial vitality plays a significant role in various dimensions influencing carbon emissions. Correlation analysis indicates that its association with carbon emissions has the strongest correlation (r = 0.639), while factor analysis further confirms the decisive impact of MBH (q = 0.7299). This suggests that the three-dimensional structure of urban space is one of the key indicators affecting urban carbon emissions. In terms of its mechanisms, architectural form affects carbon emissions through three interconnected pathways: high-rise buildings, due to vertical agglomeration effects, accommodate a large number of energy-intensive activities, thereby directly increasing energy consumption density per unit area; they also alter wind field dynamics and solar radiation efficiency, exacerbating the urban heat island effect and indirectly raising temperature control energy consumption (Tian et al., 2024). Additionally, spatial structures, such as FAR and MBH, influence the urban development process, leading to changes in urban economic sectors. High-rise, high-density areas often attract energy-intensive, capital-intensive industries, thus solidifying a high-carbon spatial pattern²⁴.

These findings suggest that urban carbon reduction strategies should prioritize the optimization of spatial forms as a core approach, constructing a fundamental spatial policy framework through precise control of building height and development intensity. In light of this, relevant departments should develop and implement comprehensive reduction strategies that are integrated with urban planning and spatial layout optimization, aiming to maximize land use efficiency in both two-dimensional and three-dimensional spaces, thereby establishing a robust framework for sustainable ecological development^53,54.

Internal differences in social vitality and the key role of transportation efficiency

Social vitality has a significant impact on urban carbon emissions, with a particularly prominent role for the road system. Factor analysis results indicate that the road accessibility indicator (integration q = 0.549) has a significantly better explanatory power than the functional mix indicators (with q values below 0.133), suggesting that the efficiency of the transportation system is crucial in shaping carbon emission patterns. This finding is particularly significant in the context of transportation in Yantai. Unlike megacities with developed rail transit, Yantai’s travel structure is primarily dominated by conventional buses and electric bicycles, which play a crucial role in daily commuting and markedly impact the urban carbon emission pattern. The integration degree indicator not only reflects walking convenience but also represents the efficiency of urban trunk road networks in supporting electric bicycles and the bus system. Therefore, enhancing the integration of the road network will directly optimize the cycling environment for electric bicycles and improve the coverage quality of bus routes, effectively guiding residents to shift from private motor vehicles to low-carbon travel modes⁵⁵.

The research results also indicate that merely increasing road density (connectivity q = 0.253) has a limited effect on carbon reduction. This finding validates the theoretical understanding that road density is necessary but not sufficient for urbanization^51,56. In contrast, enhancing the overall efficiency of the road network structure (Integration) has a more significant impact on suppressing carbon emissions⁵⁷. Therefore, road planning in Yantai should focus on optimizing the overall efficiency of the road network structure, aiming to improve connectivity among main roads, public transport hubs, and non-motorized transport networks, rather than solely pursuing road network density indicators. In terms of facility layout, the relatively high explanatory power of aggregation suggests that a moderate concentration of functions is more beneficial for reducing carbon emissions than merely increasing functional diversity. Therefore, urban planning should prioritize the reasonable aggregation of functional blocks, improving the convenience of facility usage to reduce inter-regional traffic demand and thus achieve primary emission reductions.

Based on the research results, Yantai should establish a synergistic development path that enhances vitality while reducing carbon emissions. In the future, regarding the road system, the core focus should be on integration, with an emphasis on improving the connectivity efficiency among the main road network, public transport hubs and non-motorized transport systems. Achieving this requires optimizing intersection designs and enhancing dedicated lane networks to ensure the continuity of various low-carbon travel options. In terms of functional layout, a moderate concentration strategy should be adopted to promote the organic integration of commercial, service, and residential areas. This approach aims to enhance regional vitality by increasing facility aggregation and convenience. Moreover, it should simultaneously reduce traffic demand at the source to effectively control carbon emissions. This systematic approach will effectively balance urban development with ecological protection.

The driving effect of economic vitality and the pathway for industrial transformation

Urban carbon emissions show a strong correlation with economic vitality. In this study, economic vitality is primarily assessed through the density of dining facilities (q = 0.402) and GDPpc (q = 0.471), both of which exhibit significant explanatory power for carbon emissions. First, dining facilities contribute to significant energy consumption while fulfilling production and social consumption demands. This finding should not be interpreted merely as a restriction on the development of the catering industry; rather, it highlights the urgency of reducing carbon intensity in this sector through technological advancements and management innovations. In the future, this may be achieved through the establishment of industry energy efficiency standards, mandating the promotion of high-efficiency energy-saving equipment, and advancing the complete electrification of kitchen operations to reduce direct fossil fuel use. This approach aims to establish a green catering supply chain and optimize carbon emissions in cold chain logistics and food processing stages.

At the macroeconomic level, a fundamental shift in the model of economic growth is necessary. On the one hand, it is essential to change the traditional development model that focuses on GDP growth, avoiding the excessive expansion of high-energy-consuming projects. On the other hand, it is important to actively cultivate the digital economy and green low-carbon industries⁵⁸. This can be accomplished by establishing a carbon reduction-oriented industry access mechanism and using economic tools such as taxes and credits to guide capital toward low-carbon sectors. Additionally, a more comprehensive performance evaluation system should be established to reduce dependence on a sole GDP indicator and strengthen the orientation toward green development.

Based on quantitative research findings, it is recommended to adopt differentiated regional development strategies: in central areas with high commercial vitality, the focus should be on the green renovation of existing facilities to reduce carbon emissions through equipment updates and process optimization. In newly developed areas, low-carbon construction standards must be strictly enforced to control the entry of high-carbon projects at the source. This precise governance approach can maintain economic vitality while effectively controlling carbon emissions, providing institutional support for achieving high-quality development⁵⁹.

The regulatory function of environmental vitality and the construction of ecological networks

Environmental vitality shows a stable negative correlation with carbon emissions (r = -0.475). Factor analysis results indicate that while the NDVI offers limited independent explanatory power (q = 0.362), it plays an important regulatory role through multiple pathways. First, vegetation cover directly absorbs carbon dioxide from the atmosphere through carbon sequestration. Second, green space systems significantly reduce energy consumption for cooling buildings and alleviate the urban heat island effect⁶⁰. Additionally, ecological spaces can encourage residents to adopt low-carbon travel. These mechanisms are supported by interaction analysis, which reveals a synergistic enhancement effect between NDVI and factors such as travel choices. This indicates that both natural and built environment elements jointly affect carbon emission patterns.

Based on these findings, we recommend building a multi-layered urban ecological network: by establishing connected urban ventilation corridors that organically link large ecological patches with community-level green spaces; promoting the integration of ecological and gray infrastructure design in key development areas; and using techniques like vertical greening to enhance the ecological resilience of developed areas. This “ecological foundation” planning strategy can effectively strengthen urban climate resilience and provide sustainable natural solutions for carbon reduction.

The mechanisms of cultural vitality and perceptual vitality and their low-carbon pathways

This study reveals how cultural vitality and perceptual vitality affect carbon emissions through correlation analysis and OPGD. Although their independent explanatory power is somewhat limited, this quantitative result requires deeper interpretation using urban spatial behavior theory.

From the perspective of spatial behavior, cultural facilities act as important “destination anchors”, and their spatial distribution indirectly impacts carbon emissions by shaping the structure of residents travel demand. Research indicates that when cultural facilities are strategically located near public transport hubs and commercial centers, they can effectively integrate multi-purpose travel chains, thereby reducing unnecessary trips. Empirical studies have confirmed that a rational facility layout can significantly decrease the carbon emission intensity of planned trips⁶¹.

In terms of perceptual vitality, the mechanisms related to environmental behavior play a key regulatory role. The visual quality of street spaces affects travel decisions and psychological perceptions: increasing the GVI enhances visual comfort, which in turn promotes walking continuity, while greater spatial openness extends walking distances by providing a sense of safety. Previous studies have shown that in neighborhoods where GVI is lower than 15% (and in some cases even 5%), residents are more likely to experience both physiological and psychological discomfort, which leads to a decreased willingness to walk; improving GVI to over 25% can significantly improve the walking environment⁶². Although this micro-behavioral adjustment may not directly lead to significant macro-level emission reductions, it has a long-term cumulative impact on transportation carbon emissions by consistently altering individual travel choices.

Based on the aforementioned mechanisms, it is recommended to strengthen the spatial integration of cultural facilities and transportation hubs at the facility layout level, regulating travel demand from the source through location optimization. At the same time, it is essential to systematically enhance the perceived quality of street spaces through environmental design, utilizing careful design to increase the attractiveness of low-carbon travel. It is important to emphasize that the unique value of cultural vitality and perceptual vitality lies in their characteristic of flexible regulation. In the urban low-carbon governance system, these measures—based on spatial optimization and behavioral guidance—effectively complement more rigid approaches, such as building form control and industrial structure adjustment, collectively constructing a comprehensive emission reduction framework with multiple scales and pathways. This systematic understanding not only provides a rational explanation for the quantitative research results but also serves as a theoretical basis for formulating precise low-carbon urban planning strategies.

The interactive effects of multidimensional vitality and insights for systemic governance

The correlation and analysis of multidimensional urban vitality and urban carbon emissions indicate that vitality across different dimensions has varying degrees of impact on carbon emissions³⁹. The detection of factor interactions has further revealed the complex synergy mechanisms among the driving factors. Notably, the interaction between integration and maximum building height is the strongest, indicating that the peak of urban carbon emissions is not solely caused by a single factor, but is rather an inevitable result of the spatial coupling between efficient transportation and high-intensity development.

At the same time, the interactive effects among other factors further confirm the systemic characteristics of carbon emission spatial patterns shaped by the road network, building form, commercial activities, and natural elements. Therefore, controlling measures based on a single dimension are insufficient to address the carbon emission aggregation effects resulting from the synergy of multiple factors. Urban carbon emission hotspots often occur in areas where highly integrated transportation networks intersect with high-intensity development, while ecological elements mitigate this compound effect to some extent through their carbon sink functions and microclimate regulation. The interaction between dining facilities and building form in economic vitality, as well as the synergy between cultural vitality and perceptual vitality, further emphasizes the systemic requirements for urban carbon reduction.

Significance of the study

In the context of global climate change, cities, as major sources of carbon emissions and key areas for carbon reduction, face the dual challenges of enhancing vitality and reducing carbon emissions. Accurately identifying the spatial patterns of urban carbon emissions and thoroughly revealing the impact mechanisms of urban vitality construction factors on urban carbon emissions are crucial prerequisites for the sustainable development of cities characterized by “high vitality and low carbon emissions”⁶³.

First, this study selects Yantai City as the case area. As a pilot city for urban renewal and carbon peak initiatives, Yantai can serve as a research model for other cities. The insights gained from this study can also be extended to urban contexts and stages of development. For instance, industrial cities should prioritize the regulation of factors related to industrial vitality, such as green technology innovation, while tourism cities should focus on the mitigating effects of ecological vitality on carbon emissions. This provides methodological support for low-carbon path selection in diverse cities worldwide.

Secondly, regarding the intergenerational long-term effects of optimizing urban vitality, this optimization essentially involves the sustainable allocation of spatial resources. For example, improving walkability (social vitality) can reduce dependency on private cars, with the benefits of emission reductions likely to increase as demographic structures change. The development of the digital economy (economic vitality) may reduce the marginal costs of emission reductions in future cities through technological spillover effects. Additionally, optimizing the three-dimensional architectural forms of cities can promote continuous low-carbon construction by addressing both population density and building design.

Finally, this study aligns with the United Nations SDG 11 on “Sustainable Cities and Communities” while also demonstrating the leverage of “vitality-oriented planning” in the low-carbon transition. This is consistent with the IPCC’s sixth assessment report, which advocates for “Climate-Resilient Development” providing a scientific basis for developing countries to avoid carbon lock-in during their urbanization processes.

Conclusion

This study uses urban form as a starting point to comprehensively review the research on urban vitality, urban form, and carbon emissions. Using Python scripts, deep learning algorithms and other methods to gather data from multiple sources, a theoretical framework is constructed to evaluate urban vitality from a three-dimensional spatial and a human perceptual viewpoint. Methods such as entropy-weight TOPSIS and Geodetector are employed to explore the interplay between urban vitality and carbon emissions, advancing the study of their relationships in the central urban area of Yantai. The conclusions are as follows: (1) Urban vitality in the central urban area of Yantai displays a “core-low, coastal-high” multicentre distribution pattern, with social vitality being the most crucial factor affecting urban vitality. High vitality areas have significant spillover effects, promoting the development of vitality in surrounding areas. Muping and Penglai, as secondary vitality centres, should be prioritized for development in the future. (2) There are substantial differences in how various dimensions of urban vitality influence carbon emissions. The strongest correlation is found between carbon emissions and spatial vitality, followed by social, economic, perceptual, and cultural vitality. There is a noteworthy negative correlation between environmental vitality and urban carbon emissions. (3) The explanatory power of various urban vitality factors on the spatial distribution of carbon emissions in the central urban area of Yantai is ranked as follows: maximum building height > integration > ABH > FAR > GDP per capita > sidewalk ratio > density of dining facilities > density of cultural facilities > GVI > SVF > BCR > NDVI > connectivity > richness > aggregation > disorder > choice. Overall, this indicates that spatial form-related factors have a significantly greater influence than those from other categories, suggesting that the structural characteristics of the built environment are crucial in impacting carbon emissions. (4) The interaction of urban vitality factors with carbon emissions generally exhibits a two-factor enhancement effect. Among these, the interaction of integration and MBH demonstrates the strongest explanatory power, highlighting the importance of synergy between road networks and building forms. Other notable combinations include maximum building height with the density of dining facilities and maximum building height with NDVI. These combinations reveal a complex mechanism shaping carbon emission patterns, influenced by the interplay of building forms, commercial distribution, and natural elements.

This study systematically analyzes the impact pathways and driving mechanisms of urban vitality on carbon emissions, providing empirical evidence for low-carbon-oriented urban planning. It is recommended that future efforts integrate comprehensive measures, such as appropriately controlling building heights, optimizing road network structures, balancing facility distribution, and enhancing environmental quality, to synergistically improve urban vitality while reducing carbon emissions. This would facilitate the development of low-carbon vitality demonstration zones, smart energy networks, and green low-carbon communities. It should be noted that this study is based on cross-sectional data, which effectively reveals spatial associations but makes it difficult to capture dynamic evolutionary processes. Additionally, some dimensions of the six-dimensional indicators (such as perceptual) still have room for deeper quantification, and the 1 km × 1 km grid scale may obscure micro-variations. Future research could incorporate long-term time series data and integrate multi-source big data to refine indicators and conduct comparisons at multiple scales, thereby enhancing the generalizability of the conclusions and the depth of the mechanisms explored. Furthermore, while geographic detectors primarily reveal statistical relationships, future studies could combine structural equation modeling, qualitative interviews, and other methods to further uncover the complex nonlinear mechanisms and social behavioral motivations among these factors.