Spatial–Temporal Evolution and Driving Factors of Carbon Emissions in Shrinking Cities: A Case Study of the Three Northeastern Provinces in China

Abstract

Shrinking cities are generally experiencing decreases in population, economic activity, and spatial expansion. However, whether this “low-growth” trajectory leads to an actual reduction in carbon emissions or is constrained by carbon lock-in effects and the complex interaction between urban shrinkage and carbon emissions remains unclear. To address this gap, this study examines 34 shrinking cities of the three northeastern provinces in China, utilizing nighttime light data to identify the spatial–temporal patterns of carbon emissions from a multidimensional perspective. Additionally, it explores the key drivers behind these emissions. Results show the following: (1) Spatiotemporally, carbon emissions are closely linked to shrinking cities, which also exhibit spatial–temporal heterogeneity. (2) There is a significant negative spatial correlation between carbon emissions and urban shrinkage degree (SD), with HL clusters (high–low clusters) and LH clusters (low–high clusters) being the main clustering types. (3) Through population, economic, and social driving factors, this paper identifies three synergistic effects shaping spatial–temporal carbon heterogeneity: passive reduction in economic scale (scale effect), volatility effect of structural transformation (structure effect), and spatial–institutional carbon lock-in (lock-in effect). The findings offer new insights into the low-carbon transition potential of shrinking cities and provide a basis for developing targeted policy frameworks to facilitate their sustainable transformation.

1. Introduction

As the world’s largest developing country, China faces severe carbon emission pressures during rapid industrialization and urbanization. According to the International Energy Agency, China accounts for approximately 31% of global carbon emissions [1], with 70% originating from cities [2]. Thus, urban carbon emission research is critical for achieving national low-carbon development and carbon peaking goals. Notably, some cities exhibit shrinkage phenomena—population decline, economic slowdown, and inefficient spatial utilization [3]. These shrinking cities, influenced by resource endowments, development stages, and industrial structures, display heterogeneous carbon emission characteristics and pathways, accompanied by complex energy and environmental effects [4,5]. However, this heterogeneity renders traditional emission reduction strategies designed for growing cities less applicable or even ineffective. Therefore, it is crucial to clarify the carbon emission characteristics of shrinking cities and driving mechanisms.

Recent studies on urbanization and carbon emissions mainly focus on expanding cities; related studies have indicated that urban expansion can significantly exacerbate carbon emissions, and there is remarkable regional heterogeneity in the sensitivity of carbon emissions to urban expansion. The specific impact pathways and intensities vary depending on expansion patterns, regional policies, and land-use efficiency [6,7,8]. However, research on shrinking cities remains limited. März et al. [9] first proposed mechanisms linking urban shrinkage to carbon reduction and emphasized the need to address emissions in shrinking cities. In this regard, most scholars have analyzed the spatial–temporal evolution of carbon emissions in shrinking cities, and found that carbon emissions are closely linked to urban shrinkage phases, and there are significant differences in carbon emissions in the study area of hot- and coldspots [10,11,12], and this spatial–temporal heterogeneity provides new thinking problems for the subsequent research. Based on this, most studies have explored the driving factors of this phenomenon, and it is found that the characteristics of shrinking cities—population shrinkage, economic shrinkage, and social shrinkage—have different mechanisms of effect on this phenomenon. Therefore, it is necessary to further explore the specific path and mechanism of the impact of urban shrinkage on carbon emissions.

Most of the existing studies have explored the drivers of carbon emissions in shrinking cities based on population, economic, social and other indicators related to urban shrinkage [10,11,12,13,14]. The models currently used to analyze carbon emission drivers are usually traditional econometric models; for example, Liu et al. [15] applied the ST-IDA model (Spatio-Temporal Index Decomposition Analysis) and LMDI decomposition method to decompose the spatial–temporal carbon emission drivers of the four major urban agglomerations in China, which revealed that the spatial–temporal evolution of carbon emissions mainly depended on the industrial sector; Chen et al. [16] applied the LMDI method to analyze and found that the core factors of carbon emissions in nine provinces in the Yellow River Basin are energy intensity effect and economic growth effect. As for the study of carbon emission drivers in shrinking cities, the common methods used by scholars are spatial econometric models; for example, Zhang et al. [17] found that the interaction between urban shrinkage and building land expansion is the dominant factor influencing the synergy effect of pollution reduction and carbon mitigation through the quantitative analysis of geodetic detector model, while scholars such as Yang et al. [10] proposed that the use of the Spatial Durbin Model can effectively avoid the endogeneity problem in the calculation process, and find that the drivers of carbon emissions across the three northeastern provinces in China under the shrinkage scenario are complex, and that population loss and public facilities have a positive effect on carbon emissions in the shrinking cities of the three northeastern provinces in China, while economic shrinkage and industrial structure have a negative inhibitory effect; however, some scholars have pointed out that when the model is analyzed in conjunction with the multidimensional data of the cities, the accuracy of the estimates will be affected by potential multicollinearity problem [18]; in this regard, some articles introduced the random forest model when exploring the drivers, which can not only exclude the problem of multicollinearity, but also assess the importance of the independent variables [19]; for example, Han et al. [20], in their study on the driving factors of land-use carbon emissions in the Aksu River Basin, employed a random forest model to identify human activity intensity, temperature, population density, and precipitation as the primary influencing factors. Further analysis revealed that these four factors exhibited significant spatial heterogeneity in their effects on land-use carbon emissions across the basin, providing valuable insights for this study’s exploration of the spatial–temporal heterogeneity of carbon emission drivers.

The phenomenon of urban shrinking in the three northeastern provinces in China has a multidimensional typicality, which is a landmark sample for the study of the “shrinking-carbon emission” correlation mechanism. As traditional old industrial bases, their structural characteristics reflect the common contradictions of shrinking cities: continuous population loss and deep aging have weakened the economic dynamics of the cities [21]; the industrial structure dominated by the heavy industry relies on energy-consuming industries for a long period of time, which has led to the “shrinking-high carbon” dilemma in some areas. More prominently, in the background of population loss, some cities still continue the spatial expansion pattern, and the inefficient use of built-up areas and redundant infrastructure exacerbate energy waste, revealing a serious disconnect between policy planning and shrinkage reality [22,23]. Such characteristics echo international cases such as the Ruhr area in Germany and the “Rust Belt” in the United States, highlighting the global commonality of the carbon emission problems of shrinking cities. Given that urban shrinkage represents an inevitable and widespread phenomenon [24], research on carbon emissions in Northeast China’s shrinking cities can also provide theoretical references and practical lessons for the exploration of low-carbon paths by shrinking cities around the world.

Based on the identification of shrinking cities in China’s three northeastern provinces, this study aims to address the following research objectives:

(1)

To investigate the spatial–temporal evolution patterns and characteristics of carbon emissions in 34 shrinking cities of the three northeastern provinces in China;

(2)

To reveal the spatial clustering patterns of carbon emissions and clarify the spatial correlations between the degree of urban shrinkage and carbon emission dynamics;

(3)

To identify the key driving factors underlying the spatial–temporal heterogeneity of carbon emissions, and to elucidate the pathways and interaction effects through which population scale, industrial restructuring, and institutional constraints influence such heterogeneity;

(4)

Building upon the above analyses, to assess the low-carbon potential of shrinking cities and propose targeted transition policies.

2. Materials and Methods

2.1. Study Area

The three northeastern provinces in China is defined as the provinces of Heilongjiang, Jilin and Liaoning, with a total of 36 prefecture-level cities, and are an important hub in the Northeast Asian region. The three northeastern provinces in China are endowed with superior resources, and the reserves of many strategic resources rank among the top in the country. It is an important heavy industry base and oil production base in China, and the energy industry and equipment manufacturing industry occupy an important strategic position in the national industrial layout. At present, the three northeastern provinces in China are undergoing a transitional period of socio-economic development. In recent years, GDP has continued to grow, but the growth rate has gradually declined. Although the overall built-up area has expanded, some cities are facing population shrinkage, resulting in increasing human–land conflicts and inefficient land use. The study area is shown in (Figure 1).

2.2. Research Framework

The research framework of this paper consists of three main parts (Figure 2).

2.3. Data Selection and Collection

The base map used in this study was obtained from the Ministry of Natural Resources (PRC) Map Technical Review Center’s Standard Map Service (review No. GS (2020) 4619) and was used without modification. This study selects 2010–2022 as the research period, primarily because this period covers the full implementation phase of the Northeast Revitalization Policy, enables the capture of the critical transition period of regional development, and ensures data continuity and reliability. We identify shrinking cities using permanent population (POP) and analyze the drivers of carbon emissions with ten explanatory variables: permanent population (POP), population density (PD), gross domestic product (GDP), economic growth rate (GGR), fiscal revenue (FR), secondary industry (IS), tertiary industry (IT), per capita road area (PRA), green coverage rate (GCR), and urban built-up area (UBA). All data are sourced from the statistical yearbooks of prefecture-level cities for 2010–2022 (https://www.stats.gov.cn/). The DMSP-OLS (Defense Meteorological Satellite Program-Operational Linescan System) nighttime light data are remote sensing data on nighttime lighting and are sourced from the National Oceanic Administration (NOAA) (https://www.noaa.gov/), and the software used to extract nighttime light values was ArcGIS 10.8.

2.4. Research Methodology

2.4.1. Methods for Identifying Shrinking Cities

Definition of Shrinking Cities and Urban Shrinkage Degree

Currently, there is no consensus on the definition of shrinking cities internationally. German scholar H. Häußermann first introduced the concept of shrinking cities and used the reduction in urban population size as a core indicator of urban shrinkage to describe the phenomena of population loss and economic decline in Germany caused by deindustrialization and suburbanization [25]. Subsequent studies have also typically used sustained population loss as one of the main characteristics of shrinking cities [26,27,28,29,30]. However, using population indicators alone to identify shrinking cities has limitations, as it is not comprehensive enough. Later studies suggest that urban shrinkage should also be determined by considering economic and social characteristics, such as a reduction in built-up area, economic decline, and changes in industrial structure [31,32].

The research area of this study, the three northeastern provinces of China, is the region with the most concentrated, extensive, and profound urban shrinkage in China, with issues such as population loss, spatial shrinkage, and economic decline coexisting [32,33]. This indicates that the process of urban shrinkage in the three northeastern provinces often involves multiple changes in population, space, economy, and industrial structure.

On this basis, this study defines shrinking cities as those with a decrease in permanent population and uses the urban shrinkage degree (Equation (1)) as the method for determining and identifying shrinking cities. This definition and method not only reflect the common characteristics of urban shrinkage in the northeastern region but also avoid potential collinearity issues when conducting subsequent analyses of the impacts of carbon emissions.

$${SD}_{ip}=\left({\displaystyle \frac{{POP}_{ip2022}-{POP}_{ip2010}}{{POP}_{ip2010}}}\right)$$

(1)

where ${\mathrm{S}\mathrm{D}}_{\mathrm{i}\mathrm{p}}$ denotes the shrinkage degree of city i; ${\mathrm{P}}_{\mathrm{i}\mathrm{p}2022} \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{P}}_{\mathrm{i}\mathrm{p}2010}$ represent the POP of city i in 2022 and 2010, respectively; if ${\mathrm{S}\mathrm{D}}_{\mathrm{i}\mathrm{p}}$ < 0, the city is a shrinking city, and if ${\mathrm{S}\mathrm{D}}_{\mathrm{i}\mathrm{p}}$ > 0, the city is a non-shrinking city.

Validation of Nighttime Light Data

DMSP/OLS nighttime light data has been widely recognized as an effective tool for monitoring urban dynamics, capturing variations in human social activity across different cities [34,35]. These data, to a certain extent, directly reflect the changes in human activity patterns within urban regions [36]. Therefore, we utilized nighttime light values (DN) to validate the shrinking cities in the three northeastern provinces of China. ArcGIS 10.8 was employed to extract the DN for the prefecture-level cities in the study area. To mitigate potential distortions caused by projection errors, a consistent grid resolution of 1 km × 1 km was applied. Using the prefecture-level cities in China’s three northeastern provinces as the target region, we performed saturation-correction processing and analysis of the DMSP-OLS data. An optimal quadratic regression model was established by selecting the most suitable reference images [37]. The resulting model is represented by Equation (2):

$${DN}_Y=a{DN}_X^2+b{DN}_X+c$$

(2)

where ${\mathrm{D}\mathrm{N}}_{\mathrm{Y}}$ is the gray value of the image element after correction; ${\mathrm{D}\mathrm{N}}_{\mathrm{X}}$ is the gray value of the image element before correction; $\mathrm{a}$, $\mathrm{b}$, $\mathrm{c}$ are the regression coefficients.

2.4.2. Methods for Regional Carbon Emissions Accounting

Nighttime light data exhibit a strong spatial correlation with economic activity, energy consumption, and carbon emissions. Compared with traditional accounting methods that rely on statistical data, nighttime light data—with their spatial continuity and accessibility—can more effectively capture carbon emission characteristics at the urban level. Therefore, they have been widely applied in estimating and analyzing the spatial distribution of urban carbon emissions. Moreover, nighttime light data can help address inconsistencies and data gaps in urban energy use statistics. Hence, the prefecture-level carbon emissions (${\mathrm{C}\mathrm{E}}_{\mathrm{i}\mathrm{t}})$ estimated in this study primarily correspond to direct emissions, and the predictions are based on the energy use levels reflected by the nighttime light data.

The carbon emissions of various energy sources are calculated by multiplying the energy consumption with corresponding carbon emission coefficient. To ensure a unified unit of measurement, the consumption of each type of energy is first converted into standard coal equivalents. The conversion coefficients follow the General Principles for Calculation of the Comprehensive Energy Consumption (GB/T 2589-2020) [38] and are shown in the first column of

Table 1. Accounting coefficient.

Energy Type	Conversion Coefficient to Standard Coal (kgce/kg)	Carbon Emission Coefficient (kg/kgce)
Raw Coal	0.7143	0.7559
Coke	0.9714	0.855
Crude Oil	1.4286	0.5857
Gasoline	1.4714	0.5538
Kerosene	1.4714	0.5714
Diesel Oil	1.4571	0.5921
Fuel Oil	1.4286	0.6185
Natural Gas	1.33	0.4483
Heat	34.12 *	0.67
Electricity	0.345	0.272

* The conversion coefficient for heat into standard coal is expressed in units of kgce per gigajoule (kgce/GJ).

. According to existing studies [39,40,41,42,43], the carbon emission coefficients are determined based on the 2006 IPCC Guidelines for National Greenhouse Gas Inventories issued by the Intergovernmental Panel on Climate Change (IPCC). Therefore, the provincial carbon emissions based on energy use (${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$) are calculated as follows:

$${CE}_{pro}={\displaystyle \frac{44}{12}}\times \sum _{i=1}^{10}{K}_i{E}_i$$

(3)

where ${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$ denotes provincial carbon emissions based on energy use (${10}^4$ t); ${\mathrm{E}}_{\mathrm{i}}$ denotes the energy consumption of energy type i converted into standard coal equivalents (kgce/kg); ${\mathrm{K}}_{\mathrm{i}}$ is the carbon emission coefficient for energy type $\mathrm{i}$ (kg/kgce).$\mathrm{i}$ denotes energy type, including raw coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, natural gas, heat, electricity.

Previous studies [43] have demonstrated a strong linear correlation between total carbon emissions from energy use and nighttime light data within the same region. Based on this finding, this study establishes a relationship between provincial nighttime light values (${\mathrm{D}\mathrm{N}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$) and ${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$, as expressed in Equation (4):

$${CE}_{pro}=A\times {DN}_{pro}$$

(4)

where ${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$ is the provincial carbon emissions based on energy use; $\mathrm{A}$ is the fitting coefficient; ${\mathrm{D}\mathrm{N}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$ is the provincial nighttime light values.

Finally, ${\mathrm{C}\mathrm{E}}_{\mathrm{i}\mathrm{t}}$ can be calculated based on the fitting coefficients A obtained from Equation (4). The calculation formulas for the carbon emission indicators are presented in Equations (5)–(8).

$${CE}_{it}=A\times {DN}_{it}$$

(5)

$${CI}_{it}={\displaystyle \frac{{CE}_{it}}{{GDP}_{it}}}$$

(6)

$${CP}_{it}={\displaystyle \frac{{CE}_{it}}{{POP}_{it}}}$$

(7)

$${CA}_{it}={\displaystyle \frac{{CE}_{it}}{{ARE}_{it}}}$$

(8)

where ${\mathrm{C}\mathrm{E}}_{\mathrm{i}\mathrm{t}}$ denotes the prefecture-level carbon emissions; ${\mathrm{D}\mathrm{N}}_{\mathrm{i}\mathrm{t}}$ denotes the prefecture-level nighttime light values; ${\mathrm{C}\mathrm{I}}_{\mathrm{i}\mathrm{t}}$ denotes the prefecture-level carbon emissions intensity; ${\mathrm{G}\mathrm{D}\mathrm{P}}_{\mathrm{i}\mathrm{t}}$ denotes gross domestic product; ${\mathrm{C}\mathrm{P}}_{\mathrm{i}\mathrm{t}}$ denotes the prefecture-level carbon emissions per unit area; ${\mathrm{C}\mathrm{A}}_{\mathrm{i}\mathrm{t}}$ denotes the prefecture-level per capita carbon emissions; ${\mathrm{P}\mathrm{O}\mathrm{P}}_{\mathrm{i}\mathrm{t}}$ denotes the resident population of the prefecture-level city; ${\mathrm{A}\mathrm{R}\mathrm{E}}_{\mathrm{i}\mathrm{t}}$ refers to the built-up area; prefecture-level cities are denoted by $\mathrm{i}$; time is denoted by $\mathrm{t}$.

2.4.3. Methods for Analyzing Spatial–Temporal Evolution and Driving Factors

Standard Deviational Ellipse (SDE)

SDE spatial statistics method can accurately reveal the overall characteristics of the spatial distribution of geographic elements. This method is widely used in various fields such as topographic equilibrium distribution, economic spatial pattern, and urban issues [44,45]. In this paper, SDE method is used to analyze the spatial heterogeneity characteristics of carbon emissions in shrinking cities in the three northeastern provinces in China. The formula is as follows:

Determination of the ellipse center, as shown in Equations (9) and (10).

$$\bar{X}={\displaystyle \frac{\sum _{i=1}^n{w}_i{x}_i}{\sum _{i=1}^n{w}_i}}$$

(9)

$$\bar{Y}={\displaystyle \frac{\sum _{i=1}^n{w}_i{y}_i}{\sum _{i=1}^n{w}_i}}$$

(10)

Determination of the distribution direction, as shown in Equations (11)–(14).

$$\mathit{tan}\theta ={\displaystyle \frac{\left(A+B\right)}{C}}$$

(11)

$$A=\left(\sum _{i=1}^n{w}_i^{2 }\overline{x_i^2}-\sum _{i=1}^n{w}_i^2 \overline{y_i^2}\right)$$

(12)

$$B=\sqrt{{\left(\sum _{i=1}^n{w}_i^{2 }\overline{x_i^2}-\sum _{i=1}^n{w}_i^2 \overline{y_i^2}\right)}^2+4\sum _{i=1}^n{w}_i^2 \overline{x_i} \overline{y_i}}$$

(13)

$$C=\sum _{i=1}^{n}2w_i^2 \overline{x_{i }}\overline{y_i}$$

(14)

where n denotes the number of prefecture-level cities; ${\mathrm{x}}_{\mathrm{i}}$ and ${\mathrm{y}}_{\mathrm{i}}$ denote the longitude and latitude of each prefecture-level city; ${\mathrm{w}}_{\mathrm{i}}$ denotes the carbon emissions of each prefecture-level city; ($\stackrel{\mathrm{‾}}{\mathrm{X}}$,$\stackrel{\mathrm{‾}}{\mathrm{Y}}$) denotes the weighted mean center of gravity coordinates; θ denotes the ellipse azimuth; and A, B, and C are intermediate variables used to calculate θ, representing the variance and covariance components of the spatial coordinates in the x and y directions.

Moran’s I

The Moran’s I has a significant advantage in testing global spatial autocorrelation [46], and in this paper, the Moran’s I is used to test the global spatial autocorrelation characteristics of carbon emissions in shrinking cities in the three northeastern provinces in China. The specific calculation method of Moran’s I is shown in Equation (15), while the significance test used to determine whether the results are statistically significant is adopted in Equation (16).

$${Moran}^{\prime }s\hspace{0.25em}I={\displaystyle \frac{\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}\left(x_i-\overline{x}\right)\left(x_j-\overline{x}\right)}{\sum _{i=1}^n\sum _{j=1}^n{w}_{ij}\sum _{i=1}^n{\left(x_i-\overline{x}\right)}^2}}$$

(15)

$$P=\left\{{\displaystyle \frac{\left[I-E\left(I\right)\right]}{\sqrt{Var\left(I\right)}}}\right\}\stackrel{d}{\to }N\left(\mathrm{0,1}\right)$$

(16)

where $\mathrm{n}$ denotes the number of shrinking cities; ${\mathrm{x}}_{\mathrm{i}}$ and ${\mathrm{x}}_{\mathrm{j}}$ denote the carbon emissions of shrinking cities $\mathrm{i}$ and $\mathrm{j}$, respectively; $\overline{\mathrm{x}}$ is the average value; ${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$ is the weight; ${\mathrm{M}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{n}}^{\prime }\mathrm{s}\hspace{0.25em}\mathrm{I}$ value ranges from (−1,1); less than 0 denotes a negative correlation; more than 0 denotes a positive correlation; and equal to 0 denotes an irrelevant correlation; p value denotes the level of significance; $\mathrm{E},\mathrm{V}\mathrm{a}\mathrm{r}$ and $\mathrm{N}$ denote the mathematical expectations, the variance and the normal distribution, respectively.

Hotspot Analysis

The “Getis-Ord” index (G) can be used to identify areas of high and low values of the variable in the study area by calculating the statistics, and to distinguish between “hot” and “cold” areas of carbon emissions [47]. In this paper, the local spatial autocorrelation characteristics of urban carbon emissions are analyzed by this method, and the calculation method is shown in the following equation:

$$G={\displaystyle \frac{\left[\sum _{j\ne i}^n{w}_{ij}\left(d\right)x_j\right]}{\sum _{j\ne i}^n{x}_j}}$$

(17)

where $\mathrm{G}$ denotes hotspot; $\mathrm{d}$ is the specified radius; $\mathrm{n}$ denotes the number of prefecture-level cities; ${\mathrm{w}}_{\mathrm{i}\mathrm{j}}$ denotes the spatial connectivity matrix (1 for neighboring, 0 otherwise); $\mathrm{i},\mathrm{j}$ denote a city; $\mathrm{x}$ denotes carbon emissions.

Random Forest (RF) Model

The random forest model can reflect the interaction between explanatory variables and can exclude the influence of multivariate covariance on the model. Based on the model calculation, all variables influencing the spatial and temporal differentiation of carbon emissions were ranked by their importance. The dominant factors shaping the spatial heterogeneity pattern were then identified [48]. The model evaluation indicators include the goodness of fit (${\mathrm{R}}^2$) and the root mean square error (RMSE), as shown in the following formula:

$$R={\displaystyle \frac{\sum _{i=1}^n\left(F_i-\overline{F} \right)\left(M_i-\overline{M}\right)}{\sqrt{\sum _{i=1}^n{\left(F_i-\overline{F} \right)}^2}\sqrt{\sum _{i=1}^n{\left(M_i-\overline{M}\right)}^2}}}$$

(18)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{\left(M_i-F_i\right)}^2}$$

(19)

where ${\mathrm{M}}_{\mathrm{i}}{ \mathrm{a}\mathrm{n}\mathrm{d} \mathrm{F}}_{\mathrm{i}}$ denotes the $\mathrm{i}$-th observed value and fitted value, respectively; $\overline{\mathrm{M}}$ and $\overline{\mathrm{F}}$ are the mean values of the observed and fitted values, respectively; Statistical analyses are conducted in R (version 4.3.1), 80% of the data is selected as training samples, 20% of the data is used as test samples. Through iterative cross-validation, the optimal hyperparameters were determined as 6 terminal nodes (leaf size) per tree and an ensemble of 500 decision trees.

Geographically and Temporally Weighted Regression (GTWR) Model

GTWR is a local linear regression model that can consider both spatial and temporal non-stationarity to more accurately capture spatial and temporal variations in carbon emissions, and is able to adjust the model regression coefficients based on geographic location and point in time to improve the accuracy of the prediction [49]. In this paper, the AICc law (adaptive bandwidth) in the GTWR model of ArcGIS software is applied, and the model is represented as follows:

$$y_i={\beta }_0\left(u_i,v_i,t_i\right)+\sum _k{\beta }_k\left(u_i,v_i,t_i\right)X_{ik}+{\epsilon }_i$$

(20)

where ${\mathrm{y}}_{\mathrm{i}}$ is the dependent variable of the model; ${\mathsf{\beta }}_0$ is the intercept of the formula; ${\mathrm{u}}_{\mathrm{i}},{\mathrm{v}}_{\mathrm{i}}{,\mathrm{t}}_{\mathrm{i}}$ is the value of the fitted coefficient at the $\mathrm{i}$ point; ${\mathsf{\beta }}_{\mathrm{k}}\left({\mathrm{u}}_{\mathrm{i}},{\mathrm{v}}_{\mathrm{i}},{\mathrm{t}}_{\mathrm{i}}\right)$ denotes the value of the fitted coefficient of the $\mathrm{k}$ independent variable at the $\mathrm{i}$ point; ${\mathrm{X}}_{\mathrm{i}\mathrm{k}}$ denotes the value of the $\mathrm{k}$ independent variable at the $\mathrm{i}$ point; and ${\mathsf{\epsilon }}_{\mathrm{i}}$ is the random error.

3. Results

3.1. Data Results

3.1.1. Results of Urban Shrinkage Degree Model Identification

According to the calculation of the SD model in Equation (1), the identification results of the SD of all cities in the three northeastern provinces in China from 2010 to 2022 are shown in

Table 2. Identification results of shrinking cities.

City	Shrinkage Degree (SD)	City	Shrinkage Degree (SD)
Harbin	−10.56%	Dandong	−3.52%
Qiqihar	−1.86%	Jinzhou	−4.83%
Jixi	−9.02%	Yingkou	−2.00%
Hegang	−6.81%	Fuxin	−4.52%
Shuangyashan	−3.76%	Liaoyang	−4.91%
Daqing	−5.44%	Panjin	−0.99%
Yichun	−2.09%	Tieling	−5.21%
Jiamusi	−9.09%	Chaoyang	−1.27%
Qitaihe	−16.30%	Huludao	−2.13%
Mudanjiang	−10.54%	Changchun	−1.81%
Heihe	−5.56%	Jilin	−6.77%
Suihua	−3.67%	Siping	−6.03%
Daxing’anling	−18.55%	Liaoyuan	−0.98%
Shenyang	4.97%	Tonghua	−7.64%
Dalian	2.10%	Baishan	−10.17%
Anshan	−3.41%	Songyuan	−4.70%
Fushun	−6.43%	Baicheng	−7.28%
Benxi	−6.53%	Yanbian	−8.80%

.

From 2010 to 2022, 34 out of 36 prefecture-level cities in the three northeastern provinces of China experienced varying degrees of shrinkage (as shown in Table 2), with only Shenyang and Dalian remaining non-shrinking. Overall, the urban shrinkage rate in Northeast China has exceeded 90%. Relevant calculations show that the SD of shrinking cities in the three northeastern provinces in China from 2010 to 2022 ranges from −0.98% to −18.55%. Among them, the average SD of shrinking cities in Heilongjiang Province is the highest, reaching −7.94%; Jilin Province follows with an average SD of −6.02%; and the SD of shrinking cities in Liaoning Province is relatively lower. According to the classification criteria for shrinking cities proposed by Sun et al. [50], this paper classifies the shrinking cities in the three northeastern provinces in China into five categories (Figure 3): non-shrinking cities (2), early-stage shrinking cities (8), pre-shrinking-stage cities (8), mid-shrinking-stage cities (10), and late-shrinking-stage cities (4). It can be seen that the current status of shrinking cities in the three northeastern provinces in China is mostly dominated by the mid-shrinking stage.

3.1.2. Validation Results of Nighttime Light Data

The change process of nighttime light remote sensing images in the three northeastern provinces in China from 2010 to 2022 is shown in Figure 4. From 2010 to 2022, the number of light spots significantly decreased and aggregated toward large cities, especially major cities such as Shenyang, Dalian, Changchun, and Harbin. The population distribution was mainly concentrated in the Harbin–Dalian development axis and urban agglomerations such as Harbin–Changchun Urban Agglomeration and Liaozhongnan Urban Agglomeration. During this period, the economic development of the three northeastern provinces in China was relatively lagging, traditional industrial transformation and upgrading faced difficulties, and weak urban economic growth and reduced employment opportunities led to population outflow. The shrinking cities identified by nighttime light data are spatially consistent with those calculated by population data, playing a role in identification and validation.

3.1.3. Simulation Results of Carbon Emissions from Energy

Based on the fitting between ${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$ and ${\mathrm{D}\mathrm{N}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$, the following Equation (21) was obtained, with a fitting coefficient A of 0.0215.

$${CE}_{pro}=0.0215\times {DN}_{pro}$$

(21)

Through calculation, the goodness of fit reaches 0.932, indicating a high degree of consistency between ${\mathrm{C}\mathrm{E}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$ and ${\mathrm{D}\mathrm{N}}_{\mathrm{p}\mathrm{r}\mathrm{o}}$, which can effectively meet the research needs for data analysis and result demonstration. According to Equation (5), ${\mathrm{C}\mathrm{E}}_{\mathrm{i}\mathrm{t}}$ was calculated. To verify the accuracy of the simulation, ${\mathrm{C}\mathrm{E}}_{\mathrm{i}\mathrm{t}}$ was compared with the prefecture-level city carbon emissions based on energy use, as shown in Figure 5b. The results show that the standard error between the two datasets is 21.39 million tons, with a relative error of 15.77%, indicating that the model demonstrates high fitting accuracy.

3.2. Temporal Evolution Characteristics

Figure 6 illustrates the temporal evolution trends of CE, CI, CP, and CA in shrinking cities across the three northeastern provinces of China during the study period. Overall, all four carbon emission indicators exhibited significant volatility. Specifically, CE and CP showed considerable fluctuations, while CI and CA demonstrated a gradual declining trend, reflecting the complex dynamics of carbon emissions during the urban contraction process.

The carbon emissions exhibited a rapid upward trend before 2013, with an average annual growth rate of approximately 4.9%. Starting in 2013, a significant turning point was observed, and by around 2016, four carbon-related indicators had declined to phase-specific low points. This shift can be attributed to the stringent implementation of energy-saving and emission reduction targets during the 12th Five-Year Plan, as well as industrial structural adjustments. Since the 18th National Congress of the Communist Party, the intensity of environmental regulations has steadily increased, effectively curbing the growth of carbon emissions through improved energy efficiency and accelerated de-capacity in high-carbon industries. Similar trends have been documented in the literature [51]. From 2017 onward, various carbon emission indicators showed a slight rebound and gradually stabilized. Notably, during this phase of slow recovery, the COVID-19 pandemic caused a brief decline in carbon emissions in 2020, with indicators such as carbon intensity (CI) decreasing by 1.54%. This reflects the significant short-term impact of pandemic control measures on regional economic activities, leading to a temporary reduction in energy consumption and carbon emissions [52,53,54,55]. As economic activities gradually resumed, carbon emission levels returned to a stable adjustment range by 2022, with changes in all carbon emission indicators remaining within 1% and without significant fluctuations. Overall, while the pandemic caused a temporary disruption in the carbon emission trends of shrinking cities, it did not fundamentally alter their long-term trajectory. This underscores the need for policymakers to consider the impact resilience and recovery capacity of different regions to systematically enhance carbon reduction resilience and promote sustainable development.

Furthermore, the study finds a close correlation between the temporal evolution of carbon emission indicators and urban shrinkage stages. Carbon emission indicators in late-contraction-stage cities (e.g., Harbin, Mudanjiang) remained relatively stable. In contrast, indicators in middle-contraction-stage cities (e.g., Tieling, Daqing) exhibited more pronounced fluctuations. Investigating the linkage mechanisms between carbon emission dynamics and urban shrinkage intensity provides critical insights for revealing their underlying interaction mechanisms and offers a scientific basis for formulating differentiated policies.

3.3. Spatial Evolution Characteristics

3.3.1. Spatial Distribution Pattern of Carbon Emissions

To intuitively reveal the regional disparities and spatial distribution patterns of carbon emissions, this study examines the spatial evolution of CE, CI, CP, and CA in the shrinking cities of the three northeastern provinces for 2010, 2016, and 2022 (Figure 7). From 2010 to 2022, cities with high carbon emissions were mainly concentrated in highly industrialized and energy-intensive areas such as Shenyang, Daqing, and Fushun, as well as in provincial capitals like Harbin and Changchun. In contrast, low-emission cities were mostly located in resource-depleted or peripheral areas of the three provinces. The spatial distribution of CI exhibits a gradually weakening north–south differentiation, with high-value areas expanding from the northeastern and southern regions toward surrounding cities. Nevertheless, Liaoning Province has consistently remained a high-value area of CI. In comparison, the spatial variations in CP and CA are relatively moderate, suggesting that population density and urban land scale play a stabilizing role in shaping the regional carbon emission pattern. Overall, the spatial distribution of carbon emissions in the shrinking cities of Northeast China demonstrates distinct regional differentiation and dynamic evolutionary characteristics, which are closely linked to regional economic development, population distribution, and urban land scale.

Based on a preliminary analysis of spatial distribution patterns, we find that carbon emissions in shrinking cities across China’s three northeastern provinces exhibit significant spatial heterogeneity, characterized by clear differences between cities and a dynamically evolving pattern. Relying on static distributions alone cannot reveal the spatial–temporal evolution and underlying mechanisms, and it does not clearly identify where emissions concentrate or the overall direction of change. Therefore, we employ spatial statistical methods—including Moran’s I analysis, hotspot analysis, and the SDE—to systematically examine spatial association characteristics, hotspot–coldspot configurations, and the centroid and directional trend of the spatial distribution.

3.3.2. Moran’s I-Spatial Correlation and Aggregation Analysis of Carbon Emissions

Moran’s I can effectively reveal the spatial correlation of carbon emission data, identifying whether urban emissions are clustered or randomly dispersed. Through the Moran’s I, this study explores the spatial linkage characteristics of carbon emissions in shrinking cities across the three northeastern provinces in China, offering novel insights into the spatial patterns of carbon emissions. The analysis was performed using ArcGIS 10.8 and Geoda 1.22 software, with the results (

Table 3. Moran’s value of urban carbon emissions in shrinking cities.

Year	2010	2013	2016	2019	2022
CE	0.212 **	0.403 ***	0.420 ***	0.478 **	0.344 **
	(2.6448)	(2.4944)	(2.7334)	(2.9126)	(2.12)
CI	0.557 ***	0.365 ***	0.347 ***	0.356 ***	0.333 ***
	(6.77)	(4.947)	(4.723)	(6.715)	(6.182)
CP	0.328 ***	0.366 ***	0.376 ***	0.368 **	0.307 ***
	(4.126)	(4.792)	(4.93)	(2.234)	(2.18)
CA	0.054 **	0.115 **	0.129 **	0.157 **	0.066 ***
	(2.198)	(2.329)	(2.462)	(2.18)	(2.35)

***: p < 0.01; **: p < 0.05. The numbers in brackets represent the z-values.

) indicating statistically significant Moran’s I (p < 0.05) and Z-values (>1.96) for all four indicators across the study period. These results suggest a strong positive spatial correlation and a non-random distribution of carbon emissions. The findings show that CE, CP, and CA consistently formed spatial clusters over the study period. While CI also exhibited spatial correlation, it demonstrated a clear declining trend, indicating a weakening of spatial clustering for CI. In summary, the spatial correlation patterns of carbon emissions in the shrinking cities in the three northeastern provinces in China display significant heterogeneity. At the spatial scale, Moran’s I analysis shows that the spatial distribution of carbon emissions during the study period is not random, but shows significant spatial clustering characteristics, which provides support for the subsequent investigation of the driving factors of carbon emissions.

3.3.3. Coldspot and Hotspot Analysis—Spatial Heterogeneity in Data Distribution

Coldspot and hotspot analysis enables a more precise understanding of spatial heterogeneity in carbon emissions among shrinking cities in the three northeastern provinces in China. By applying the Getis-Ord G statistic, this method accurately identifies “hot spot” and “cold spot” regions. It further analyzes the spatial distribution of high-emission and low-emission zones in depth, complementing and refining our comprehension of carbon emission spatial patterns. These insights provide critical evidence for formulating differentiated carbon management strategies. Figure 8 reveals the spatial heterogeneity characteristics of hotspots and coldspots and the dynamic evolution patterns of carbon emissions (CE, CI, CP, CA) in shrinking cities across the three northeastern provinces in China. The integrated spatial–temporal analysis reveals that the spatial patterns of carbon emission hotspots and coldspots in the study area exhibit notable heterogeneity. Hotspots are predominantly concentrated throughout Heilongjiang Province, while coldspots are mainly distributed within Liaoning Province. Specifically, the spatial evolution characteristics of different carbon emission dimensions are as follows: From the distribution of hotspots and coldspots in Total CE, the spatial pattern exhibits distinct characteristics of expansion and movement. During the study period, the spatial centroid of CE hotspots gradually shifted eastward from the central urban area of Harbin City and its western periphery, and later exhibited a trend of northwestward radiation and diffusion. Both the hotspots and coldspots of CI showed a contracting trend. The hotspots gradually contracted from northern Heilongjiang Province to localized northern areas, while the coldspots remained predominantly concentrated in Liaoning Province and progressively stabilized.

The spatial heterogeneity of CP indicates that coldspots are concentrated in Liaoning Province, while hotspots gradually diverged into two sub-clusters in the northwest and eastern regions, exhibiting significant spatial dispersion. For CA, spatial concentration has intensified, with hotspots contracting and concentrating from the central-western Heilongjiang Province toward the northwest, while the spatial constraint effect of coldspots progressively weakened. Overall, the spatial patterns of carbon emission hotspots and coldspots in shrinking cities across the three northeastern provinces in China exhibit significant stability: hotspots remain persistently anchored in the high-latitude northern regions, with only minor spatial shifts. Coldspots remain fixed in the southern part of Liaoning Province.

3.3.4. SDE—Directional Distribution and Spatial Dispersion of Spatial Data

This chapter leverages the standard deviational ellipse method to conduct an in-depth analysis of the spatial distribution direction, clustering patterns, and degree of dispersion of carbon emissions in shrinking cities across the three northeastern provinces in China. It precisely identifies core zones and peripheral areas of carbon emissions, providing critical evidence for further exploration of their spatial dynamics and the formulation of targeted mitigation strategies. Figure 9 illustrates the spatial dispersion characteristics of carbon emission indicators (CE, CI, CP, CA) in shrinking cities across the three northeastern provinces in China. Overall, the major axes of the standard deviational ellipses for the four carbon emission indicators (CE, CI, CP, CA) exhibit a “northeast-southwest” orientation and are predominantly located in the central region of the three northeastern provinces in China. From a temporal perspective, there are significant overall dynamic changes. Post 2016, the spatial centroid of the standard deviational ellipse shifted significantly compared to the earlier period and gradually moved westward. Concurrently, high-emission zones have increasingly converged in the three northeastern provinces in China, centered around Suihua and Heihe. The above evolution characteristics indicate that the spatial distribution pattern of carbon emissions in shrinking cities of the three northeastern provinces in China shows significant dynamic adjustment characteristics. This phenomenon of spatial restructuring is closely linked to the geographic reorganization of carbon emission sources driven by factors such as industrial relocation and energy mix restructuring in the three northeastern provinces in China. It also reflects systemic shifts in the geographic distribution of carbon emissions during the region’s low-carbon transition.

3.3.5. The Spatial Correlation Between Urban Shrinkage and Carbon Emissions

To better analyze the spatial correlation patterns between shrinking cities and carbon emissions in the three northeastern provinces in China from 2010 to 2022, a bivariate spatial autocorrelation analysis was conducted using GeoDa to examine the spatial relationships between urban shrinkage intensity and both carbon emission intensity and total carbon emissions.

As shown in Figure 10, the local Moran’s I of −0.252 indicates a significant negative spatial correlation between SD and CI. According to the LISA cluster map, there are no HH clusters (high–high clusters) in the study area where both urban shrinkage intensity and carbon emission intensity are significantly high. Although traditional old industrial cities with high carbon emissions (such as Changchun and Shuangyashan) have relatively high carbon emission intensity, due to the welfare inertia of resource-based cities and their complete public service systems, population loss is not obvious, lagging relatively behind the process of industrial recession. The clustering trend of LL clusters (low–low clusters) is relatively pronounced, primarily distributed in cities such as Qiqihar, Suihua, and Daqing in western Heilongjiang Province. These cities form the “western wing” economic belt of the three northeastern provinces in China, characterized by a more optimized industrial structure, stronger population attractiveness, and higher carbon emission efficiency. The LH clusters (low–high clusters) cover a relatively small area, primarily distributed in central Liaoning Province. These cities rely heavily on heavy industries (machinery, steel), and despite no significant population shrinkage, their energy-intensive industrial structures have resulted in persistently high carbon emission intensity. The HL clusters (high–low clusters) are relatively dispersed in spatial distribution, concentrated in Heihe, Tonghua, and Jilin. Due to the decline in traditional resource-based industries and delayed economic transition, these cities have experienced persistent outflow of young and working-age labor, exacerbating population shrinkage. Concurrently, the contraction or shutdown of legacy energy-intensive industries has led to a subsequent decline in carbon emission intensity.

3.4. Drivers of Spatial–Temporal Heterogeneity in Carbon Emissions

3.4.1. Model Variables

In this section, based on the multi-layered dimensions of the drivers of spatial–temporal heterogeneity of carbon emissions, combined with the special characteristics of shrinking cities and relevant basis, and referring to related studies, CI is selected as the explanatory variable of the paper [56], and 10 explanatory variables are selected from the three dimensions of population, economy, and society in order to analyze the mechanism of spatial heterogeneity of carbon emissions, as shown in

Table 4. Descriptions of model variables.

Aspect	Variable	Variable Description	Unit
Population	Permanent Population (POP)	Year-end permanent population within city administrative areas	104 persons
	Population Density (PD)	Ratio of total population to built-up area	persons/km2
Economy	Gross Domestic Product (GDP)	Total economic output of the city	108 yuan
	Economic Growth Rate (GGR)	Annual GDP growth rate of the city	%
	Fiscal Revenue (FR)	Total local fiscal revenue	108 yuan
	Secondary Industry (IS)	Proportion of secondary industry output in GDP	%
	Tertiary Industry (IT)	Proportion of tertiary industry output in GDP	%
Society	Per Capita Road Area (PRA)	Average road area per capita in the city	m2/person
	Green Coverage Rate (GCR)	Proportion of green area in built-up area	%
	Urban Built-up Area (UBA)	Total built-up area within city boundaries	km2

:

The spatial–temporal heterogeneity of carbon emissions in shrinking cities is affected by multiple factors, and to avoid the influence of multivariate covariance, this paper assesses the importance of each driver through the random forest model and screens the dominant factors affecting the spatial–temporal heterogeneity of carbon emissions [48]. The 10 variables were counted to a 1 km grid by the partition statistics tool in ArcGIS, followed by z-score standardization. Model performance was assessed using ${\mathrm{R}}^2$ and RMSE. A scatter plot comparing the fitted and calculated CI values (Figure 11) reveals that all models achieved ${\mathrm{R}}^2$ values exceeding 0.92 and demonstrated high precision, with RMSE values below 0.25. Figure 12 shows the importance ranking of the drivers; MSE is used as the basis for ranking—the larger the value, the more important the driver is; the results show that POP is the dominant factor of the population dimension, FR, GDP, and IS are the dominant factors of the economic dimension, and UBA is the social dimension of the dominant factor. Therefore, the above five variables are selected as the explanatory variables of the spatial–temporal variations in carbon emissions, and the spatial driving mechanism of carbon emissions in shrinking cities in the three northeastern provinces in China is deeply analyzed by the GTWR model.

3.4.2. Spatial–Temporal Heterogeneity of Drivers

The GTWR model and OLSs model are compared and analyzed by ArcGIS, and the goodness of fit (${\mathrm{R}}^2$) and bandwidth (AICc) of the drivers under the two models are calculated, respectively. The results (

Table 5. Comparison of OLSs and GTWR.

Model	${\mathbf{R}}^2$	$\mathbf{Adjusted} {\mathbf{R}}^2$	AICc
OLSs	0.896	0.007	8140.257
GTWR	0.928	0.120	540.137

) indicate that the GTWR model exhibits higher ${\mathrm{R}}^2$ values and lower AICc values compared to the OLS model, which proves that the GTWR model has a better fitting effect and is more suitable for the study of the drivers of spatial–temporal heterogeneity of carbon emissions in shrinking cities, and has a more ideal explanation of the spatial–temporal heterogeneity mechanism.

The influence of five drivers on the spatial–temporal heterogeneity of carbon emissions is visualized and analyzed by the GTWR model, and the spatial distribution of the regression coefficients of the indicators is shown in Figure 13. The intensity and direction of the role of each driver of spatial–temporal heterogeneity are different.

The regression coefficient of FR is positive overall, and the positive influence gradually expands from the western Liaoning province to the north to the whole northwestern cities of the three northeastern provinces in China, which indicates that the level of fiscal revenue has a significant positive contribution to the spatial–temporal heterogeneity of carbon emission intensity, with the influence strengthening over time and spatially extending toward eastern regions.

The spatial distribution of regression coefficients for IS shows that areas with positively high values are primarily concentrated in the northern part of Heilongjiang Province and the western cities of Liaoning Province, and shows a tendency of gathering to the north, but the influence of IS on the spatial–temporal heterogeneity of carbon emissions is gradually weakening in the Liaoning province, which reveals that Liaoning province has made great efforts to optimize the industrial structure in the course of its economic development, and has achieved remarkable results in the adjustment of the industrial structure.

According to the spatial distribution of the GDP regression coefficient, it can be seen that the economic level has a significant negative inhibitory effect on the spatial–temporal heterogeneity of carbon emissions, showing a decreasing trend in the east–west direction, and the intensity of the negative effect shows a contraction trend during the study period, and the influence of the economic level on the spatial–temporal heterogeneity of carbon emissions is gradually weakened, which indicates that the regional coordinated development of the three northeastern Provinces in China and the optimization of the economic structure have played a positive role in the reduction in carbon emissions.

UBA’s regression coefficients exhibit notable volatility. Specifically, its negative influence on carbon emission heterogeneity has progressively diminished and, starting in year 2016, has shown a shift toward a positive effect. The regression coefficients show obvious north–south heterogeneity, with positive influence dominating in the north and negative influence dominating in the south.

In contrast to the UBA, POP exhibited strong positive effects in the southern regions (Jilin and Liaoning provinces), while negative effects were prominent in northwestern Heilongjiang Province. This pattern is mainly attributed to the relatively lagging economic development, limited employment opportunities, and the more serious phenomenon of population loss in these areas. The low level of economic activity leads to lower levels of energy consumption and carbon emissions. After 2016, the three northeastern provinces in China are subject to the double pressure of population loss and the decline in the natural growth rate, the population growth gradually stagnating or even turning negative, and a large number of labor force loss, which makes it difficult to play the negative role of the population factor on carbon emissions, and the negative effect gradually disappears.

4. Discussion

4.1. The Importance of Identifying Shrinking Cities

The emergence of shrinking cities poses a significant challenge to the traditional “growth-oriented” urban development concept [57]. In these cities, growth objectives are inconsistent with actual development conditions, lacking resource support to achieve vitality and struggling to realize revitalization goals based on their own resources. Many studies have researched the identification and classification of shrinking cities, as accurate and scientific identification and classification serve as the foundation and key to related research. However, the shrinking processes and patterns vary among cities of different scales, causes, and positioning. Currently, there is no unified academic consensus on the identification of shrinking cities. The commonly used identification method in academia is based on population indicators, which is widely applied due to its simplicity and operability. However, population data itself has inherent lag and volatility, and is prone to errors in research. It is worth noting that some scholars have proposed establishing multidimensional identification indicators to define shrinking cities, commonly including population, economic, social, and spatial indicators [58]. Although the multidimensional indicator system significantly enhances the scientificity and comprehensiveness of identifying shrinking cities, limitations still exist in data timeliness, objective consistency, and dynamic process monitoring. In particular, traditional statistical indicators are often lagging and insufficiently intuitive in capturing changes in the intensity of urban instant economic activities and human settlement density. Therefore, this paper proposes a dual verification method for identifying shrinking cities. This method first identifies shrinking cities based on population data and then conducts secondary verification through nighttime light data. With its unique advantages of timeliness, objectivity, spatial visibility, and large-scale coverage, nighttime light remote sensing data, constructing a “multi-source data fusion” identification and verification method can not only improve the accuracy and reliability of identification but also deepen our understanding of the dynamic processes and spatial patterns of urban shrinkage, providing a more solid data foundation for scientifically addressing urban shrinkage challenges [59,60].

Therefore, we also recognize that when identifying shrinking cities, regional contexts and temporal characteristics should be considered, and progressive and dynamic methods should be adopted for identification and classification [57].

4.2. The Driving Factors of Carbon Emissions in Shrinking Cities

Section 4.1 proposes that research on shrinking cities should adopt a progressive and dynamic perspective. Accordingly, this study integrates the RF and GTWR models to conduct an in-depth analysis of the driving factors underlying the spatiotemporal heterogeneity of carbon emissions in shrinking cities from 2010 to 2022. The analysis systematically reveals the strength, direction, and evolution patterns of these driving factors across space and time. The findings indicate that although the COVID-19 shock in 2020 caused periodic fluctuations in carbon emissions, it did not alter the overall trends and driving mechanisms of the spatial–temporal patterns of carbon emissions.

This study found that FR and GDP exert a relatively strong explanatory power on carbon emission intensity, showing a positive effect. This aligns with the findings of Guo et al. [11], which identified economic contraction as the primary driver of spatial variations in carbon emissions. It also corroborates the observation that economic decline in shrinking cities is often accompanied by inefficient energy use and an increase in per-unit carbon emissions [61]. Notably, related research offers explanations for this “structural trap within economic path dependency”: income growth in shrinking regions often relies on high-carbon traditional industries (such as heavy industry), easily leading to a self-reinforcing “carbon lock-in” [62]. This explains why the promoting effect of fiscal revenue on emissions continues to strengthen despite population decline.

Although previous studies generally viewed POP as a factor reducing carbon emissions [17], the GTWR model in this paper reveals that the population factor exhibits opposite effects in different regions of the three northeastern provinces in China. These regional disparities in the relationship between spatial development and carbon emissions further confirm that economic recession and population loss do not necessarily lead to a reduction in carbon emissions [63]. This challenges the view that population loss inevitably leads to regional carbon emission reduction and raises a new question: why do shrinking cities in less-developed regions achieve a win–win outcome of low-carbon and compact development, while more economically advanced regions face a “shrinkage-high carbon emission” dilemma? The detailed mechanisms underlying these divergent effects warrant in-depth exploration and research in the future.

4.3. Carbon Emission Driving Mechanisms Under the Triple Effects

This study investigates the drivers of carbon emission heterogeneity by integrating RF and GTWR models. Notably, in shrinking cities, economic recession, industrial restructuring, spatial expansion, and institutional shifts collectively exert three distinct effects on CI, converging on a core insight: In cities experiencing economic and population shrinking, the dynamics of carbon emissions do not follow a singular linear logic but are the result of the complex interplay and superposition of multiple forces. Traditional single-factor analyses or simplistic assumptions equating “shrinkage with emission reduction” are insufficient to explain this complexity. To systematically unravel these intertwined and often conflicting driving forces, we synthesize related findings to propose an integrated explanatory framework. We identify and distinguish three core mechanisms shaping carbon emission changes in the context of shrinking cities: the Scale Effect, the Structure Effect, and the Lock-in Effect.

4.3.1. Scale Effect (Passive Reduction in Economic Scale)

Economic recession in shrinking cities typically leads to a shrinkage in production and consumption scales, passively impacting energy consumption and associated carbon emissions. GTWR results revealed that GDP exerted a significant negative (suppressing) effect on CI, confirming the positive role of economic vitality in enhancing energy efficiency and reducing carbon intensity, indicating partial decoupling potential. However, a lack of economic vitality is common in many shrinking cities. Severe regional economic recession further constrains the scale of economic activity, becoming a primary driver behind the stabilization or even decline in CI in severely shrunk cities (e.g., Harbin, Mudanjiang). This “natural emission reduction” driven by the passive shrinkage of economic scale constitutes the essence of the Scale Effect.

4.3.2. Structure Effect (Volatility Effect of Structural Transformation)

Focusing on the impact of economic structural transformation on carbon emissions in shrinking cities, this study finds this transformation is often nonlinear and fluctuating. GTWR analysis identified IS as a key driver of carbon emissions, with its positive effect on CI being pronounced and spatially clustered. This highlights the persistent influence of historical legacy industrial bases and the arduous path of regional decarbonization, where over-reliance on secondary industries creates strong path dependency. Although the positive effect of IS weakened in some areas (e.g., Liaoning), the inherent industrial structure remains a major obstacle to regional decarbonization across the three northeastern provinces in China overall.

4.3.3. Lock-In Effect (Spatial and Institutional Carbon Lock-In)

Amid relatively stable spatial patterns and institutional frameworks, many shrinking cities remain locked into high-carbon development pathways. Spatially, the GTWR model reveals that UBA initially exhibited a negative (suppressing) effect on CI, but this effect has been continuously weakening and transitioned to positive values starting in 2016. This signifies a fundamental shift in the impact of UBA on CI-transitioning from a suppressing factor to a driving factor-and reflects the intensifying spatial carbon lock-in effect. Institutionally, GTWR revealed that FR exerts a significant positive effect on CI, serving as a core driving indicator. The disconnection between institutions and on-the-ground realities is the institutional root of this spatial lock-in. High regional government dependence on fiscal revenue from carbon-intensive industries increases the difficulty of carbon reduction and hinders industrial transition, creating a vicious cycle that traps shrinking cities in a carbon lock-in trap characterized by intertwined spatial and institutional constraints.

The findings demonstrate that for the three northeastern provinces in China, these three effects are not mutually exclusive but are deeply intertwined, jointly shaping the spatial–temporal heterogeneity of carbon emissions in shrinking cities.

4.4. Limitations and Future Research Directions

Building upon the preceding discussion, it is necessary to acknowledge several limitations of this study and potential directions for future research.

First, the measurement and identification of urban shrinkage involve a complex and multidimensional indicator system. This study identifies shrinking cities primarily based on population indicators and nighttime light data, without incorporating additional dimensions such as economic, social, and spatial factors. Although this dual-source identification method enhances objectivity and timeliness, it still simplifies the comprehensive nature of urban shrinkage. Future studies should therefore focus on developing a more refined multidimensional urban shrinkage identification framework that integrates population, economic, social, and spatial dimensions, thereby improving the accuracy, comparability, and robustness of urban shrinkage classification.

Second, the driving factors of carbon emissions in the context of urban shrinkage remain a complex and profound research topic. While this study explores the spatial heterogeneity of carbon emissions from multidimensional perspectives—population, economy, and society—the underlying mechanisms through which population mobility and urban contraction influence energy consumption structures and carbon emission dynamics are not yet fully understood. Future research should deepen the exploration of the dynamic interactions and feedback loops among population shrinkage, industrial restructuring, and carbon emissions, as well as their spatial–temporal coupling mechanisms.

Overall, future efforts should aim to bridge the gap between theoretical modeling and practical governance by incorporating institutional and behavioral dimensions into carbon emission analyses. A more comprehensive understanding of these relationships will provide stronger theoretical and empirical support for achieving low-carbon and sustainable development in shrinking cities.

5. Conclusions and Policy Recommendations

5.1. Conclusions

(1)

On the temporal scale, we observed significant fluctuations in total CE and carbon intensities related to economy, population, and space (CI, CP, CA) during the study period. Specifically, CE and CP showed considerable volatility, while CI and CA demonstrated a gradual declining trend. Importantly, our analysis of the 2019–2022 period reveals that the pandemic shock exerted notable impacts on carbon emissions. These findings indicate that carbon emissions during urban shrinkage exhibit non-stationary characteristics over time, influenced by multiple factors, and reveal the complex interactive relationship between socio-economic development and carbon emissions in shrinking cities.

(2)

On the spatial scale, employing spatial analytical methods including Moran’s I, hotspot analysis, and standard deviational ellipse, we identified significant spatial clustering of carbon emissions during the study period. This clustering was characterized by a distinct regional differentiation pattern of “north high-south low”. Notably, the Moran’s I value of CI demonstrated a clear declining trend, accompanied by a contraction in the spatial extent of CI hot- and coldspots, indicating a gradual weakening of CI’ s spatial clustering. To further analyze the spatial correlation pattern between CI and SD, bivariate spatial autocorrelation (LISA) analysis revealed a significant negative spatial correlation between CI and SD, with HL-type (High–Low) and LH-type (Low–High) clusters being the predominant spatial association types. This finding contrasts with the conventional view that shrinking cities universally exhibit “high-carbon lock-in” characteristics, highlighting the multifaceted nature and spatial heterogeneity of the impact of urban shrinkage on carbon emissions.

(3)

To further investigate the driving factors behind this spatial heterogeneity in carbon emissions, this study integrated RF and GTWR models. The results indicate that the spatial–temporal heterogeneity of carbon emissions is the outcome of a triple effect: Scale Effect Dominates Passive Emission Reduction: the contraction of economic scale is the primary driver of carbon emission reduction in shrinking cities. Fluctuations in Industrial Restructuring Exacerbate Spatial–Temporal Heterogeneity: over-reliance on secondary industries creates significant path dependence and barriers to transformation, intensifying spatial–temporal variations in emissions. Lock-in Effect Constrains Low-Carbon Transition: dual spatial and institutional lock-in constitute the key mechanism behind the “shrinkage-high carbon” paradox, leading to regional vicious cycles and carbon lock-in traps.

In conclusion, the evolution of carbon emissions in shrinking cities of the three northeastern provinces in China results from the spatial–temporal superposition of these three effects. Under their combined influence, the unsustainability and uncertainty of achieving low-carbon emission reduction in shrinking cities are amplified. This finding challenges the traditional assumption that shrinkage inevitably leads to decarbonization and elucidates the formation mechanism of the “shrinking-high carbon” dilemma.

5.2. Policy Recommendations

Based on the above conclusions, this subsection provides scientific recommendations for smart shrinkage and low-carbon governance strategies in shrinking cities of the three northeastern provinces in China:

(1)

Implement differentiated low-carbon transition paths and accurately align with urban shrinkage stages. Research findings indicate a close correlation between carbon emission evolution characteristics and urban shrinkage phases. For the middle-contraction-stage cities, the focus should be on “seeking progress while maintaining stability” through scientifically assessing industrial transition risks, systematically phasing out high-carbon industries, and cultivating replacement industries. For the late-contraction-stage cities, the emphasis should be on “quality improvement and efficiency enhancement” by upgrading energy system efficiency and strengthening carbon sequestration capacity. This approach effectively enhances urban emission reduction efficiency while mitigating potential risks during the transition process.

(2)

Construct a regional carbon emission reduction resilience system to cope with sudden external shocks. Research shows that the “decline-rebound-adjustment” fluctuation in carbon emission indicators during the pandemic verifies the necessity of establishing such a resilience system. It is recommended to establish a regional carbon emission monitoring and early warning system, develop graded and categorized emergency response plans, and enhance the overall carbon reduction resilience and sustainable development capacity of shrinking cities through measures such as building a diversified industrial system and optimizing energy reserves.

(3)

Take industrial structure upgrading as the core and strengthen fiscal support to alleviate the “high-carbon lock-in” effect. The paper shows that IS and FR dominate the spatial heterogeneity of carbon emissions. It is recommended to promote the transformation of traditional heavy industries toward low-consumption and high-efficiency models, leveraging digital and green technologies for empowerment; increase fiscal and tax support for new energy and other emerging industries, cultivate low-carbon clusters, and alleviate the “high-carbon lock-in” effect.

(4)

Promote multi-stakeholder collaborative development in carbon emission governance to break free from single-path dependence on government finance. At present, governance relies on government investment. In the future, it is necessary to shift to a collaborative model of “government-market-society”. Through policies such as establishing special funds and implementing differentiated taxation, diverse stakeholders can be guided to participate in carbon emission governance.

(5)

Formulate zoned and classified refined control strategies for cold–hot zones to achieve regional coordinated development. The results of the GTWR model indicate that the spatial heterogeneity of carbon emissions is influenced by multidimensional factors such as economy, population, and society. Based on the spatial heterogeneity characteristics of carbon emissions, the recommendations are as follows: build cross-departmental governance platforms and integrate monitoring and evaluation systems; strengthen industrial emission reduction technologies in northern hotspot areas; explore ecological compensation in southern coldspot areas; and implement zoned precision strategies.