An EG-Tree Model Incorporating Spatial Heterogeneity for Analyzing Multifactorial Coupling Effects on Carbon Emissions Across Industries and Regions in China

Abstract

With the proposal of the dual carbon goals, it is of great significance to identify the causes of carbon emissions and reduce carbon emissions directly. There is a lack of analysis on the causes of carbon emissions considering the coupling effect of multiple factors and regional heterogeneity. The causes of carbon emissions are examined from multiple perspectives utilizing the panel data spanning from 1997 to 2022, encompassing 30 provinces in China. To further analyze the causes of carbon emissions, an enhanced feature and regularized gradient boosting tree (EG-Tree) model is constructed, and a scoring method for the tree structure is proposed. The coupling effect of multiple factors are analyzed such as coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, natural gas, etc., on the carbon emission intensity of various industries and their regional heterogeneity. The results show that: (1) The EG-Tree model constructed in this study could accurately analyze the causes of carbon emissions under the coupling of multiple factors based on the cumulative iterative feature branching contribution values (impact factors), with an average model fitting precision of 0.30. This means the carbon emission intensity values were predicted by various industries in different regions based on different energy consumption levels and industry-specific carbon emissions, compared with the carbon emission intensity values calculated using the carbon emission measurement dataset. (2) The consumption of coal and coke has a significant impact on the average carbon emission factors of various industries, with values of 7139.95 and 7217.05, respectively. The consumption of natural gas and liquefied petroleum gas has a smaller impact on the average carbon emission intensity of various industries under the EG-Tree model with corresponding carbon emission intensity impact factors of 5057.90 and 2789.57, respectively. (3) The Northeast region is a low-carbon area, while the East region is a high-carbon area, with total carbon emissions of 2,238,646.60 million tons and 5,566,314.00 million tons of CO₂, respectively. The Northeast region has the lowest pollution intensity for heating and cooling, with carbon emissions of 155,661.73 million tons of CO₂; the industrial carbon emissions in the East region are relatively high at 1,623,835.62 million tons of CO₂. The research findings of this study are beneficial for relevant departments to focus on the main impact factors of carbon emissions in different regions and industries, and to develop targeted emission reduction policies.

1. Introduction

With the substantial consumption of traditional fossil fuels, the levels of methane (CH₄) and carbon dioxide (CO₂) continue to rise [1]. Greenhouse gas (GHG) emissions are a global concern, particularly carbon dioxide (CO₂) emissions [2]. In 2023, China’s carbon dioxide emissions ranked first globally, reaching 12.6 billion tons, accounting for approximately 34% of global carbon dioxide emissions [3]. With the proposal of China’s carbon peak and carbon neutrality goals [4], exploring the causes of China’s carbon dioxide emissions has become the primary task for carbon emission reduction work. Population, economic development, and technology are the main factors influencing anthropogenic carbon emissions [5]. The causes of carbon emissions are intricate and complex, with significant differences existing across different regions and industries. This study conducts an analysis of the causes of carbon emissions by considering regional heterogeneity based on the coupling of multiple factors.

Extensive research has been conducted in existing literature on the sources of carbon emissions. Xu et al. [6] found that the primary contributor to CO₂ emissions is fossil fuel consumption, with coal consumption accounting for as high as 82% of the total. Global CO₂ emissions from fossil fuels have increased to 36.3 billion tons [7], nearly one-third of which comes from China. As the world’s largest carbon emitter today [8], China faces enormous pressure to reduce emissions and shoulder more responsibility in this regard. Xiao et al. [9] found that industrial production and daily usage have consumed a large amount of fossil fuels such as petroleum and coal, resulting in severe greenhouse gas emissions. Chen et al. [10] indicated that the industrial, construction, transportation, and agricultural sectors are regarded as the four pillars of energy consumption, accounting for approximately 88.22% of China’s total carbon emissions. Zhang et al. [11] found that China’s industrial carbon emissions amounted to 4.695 billion tons of carbon dioxide, accounting for 52.75% of the total carbon emissions. Therefore, controlling carbon emissions in the industrial sector is a key task for achieving low-carbon economic development in China [12]. The aforementioned studies have analyzed the main causes of carbon emissions, but the types of energy sources and industries considered are not comprehensive enough. The causes of carbon emissions are intricate and complex, not solely resulting from the simple action of a single factor. Existing research lacks an analysis of the causes of carbon emissions under the coupling effects of different factors. The consumption of nine types of energy sources, including coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas, as well as energy consumption in six industries, respectively, include the transportation and construction industry, industrial sector, agriculture and forestry industry, resource recycling industry, purchased electricity industry, and the heating and cooling industry, is considered in this study. The interactions among the relevant impact factors and the main causes of carbon emissions are quantitatively assessed by the EG-Tree Model.

Existing studies have found that carbon emissions exhibit regional heterogeneity in different areas. Li et al. [13] employed various methods such as regional difference analysis and stepwise regression analysis to investigate the spatial disparities in carbon emissions and their impact factors across 286 prefecture-level and above cities in China and found significant differences in carbon emissions among different regions and sectors. Wei et al. [14] studied the spatial heterogeneity of the impact of population structure on urban carbon emissions and found significant differences in the effects of labor ratio and dependency ratio on carbon emissions between coastal cities and northeastern cities. Zhang et al. [15] found that rural carbon emissions exhibit regional disparities within a small scope. Han et al. [16] discovered that urbanization has increased per capita carbon emissions, particularly with significant effects in the eastern and central regions. Zhang et al. [17] divided China into eight economic regions and utilized methods such as GIS visualization, Theil index decomposition, and Geodetector to investigate the driving factors influencing the spatial heterogeneity pattern of regional carbon emissions. Shao et al. [18] found that various land-use types have significantly different impacts on carbon emissions and storage; industrial and construction land account for 35% and 28% of total emissions, respectively, while forest and park land account for 45% and 30% of carbon storage, respectively. The aforementioned studies indicate that the distribution of carbon emissions varies significantly across different regions. However, existing research primarily focuses on the impact of regional heterogeneity on carbon emissions, overlooking the coupled influence of carbon emissions caused by different energy categories across various regions and industries. The coupling effect of multiple factors is considered, and regional heterogeneity is incorporated to deeply analyze the causes of carbon emissions in this study.

There are numerous studies on carbon emission prediction based on decision tree models. Alpan et al. [19] developed a training model using the globally applied decision tree (DT) algorithm. This model can intervene in devices connected to the global model to reduce and stabilize annual carbon emissions at a targeted rate, achieving a 21% reduction in carbon emissions. In addition to the application of the decision tree model as mentioned above, in specific industries, Cheng et al. [20] proposed an improved genetic algorithm-based decision tree (IGA-decision tree) algorithm to enhance the accuracy of system carbon emission prediction, thereby addressing the challenge of energy conservation and emission reduction for sustainable development in oilfield enterprises. Not long ago, Li et al. [21] utilized decision trees and ensemble learning to predict the average CO₂ column concentration. In the aspect of processing carbon emission data with tree models, O’Reilly et al. [22] found that the decision tree algorithm has advantages in partitioning and statistically analyzing data. However, Jin et al. [23] conducted an analysis and summary of the carbon emission prediction models so far and found that there are still areas for improvement. At present, in the application of decision tree models for carbon emission reduction interventions and carbon emission volume predictions, there are frequently challenges, such as a propensity for overfitting and an absence of synergistic effects. This study aims to study the decision tree model in processing various types of energy carbon emission prediction data and carbon emission volumes across different industries, and to enhance the model by overcoming existing deficiencies.

In summary, the primary sources and contributing factors of carbon emissions have been investigated in the aforementioned literature, with regional heterogeneity being considered in some studies. However, the factors consider in the existing literature for the analysis of the causes of carbon emissions are relatively singular, and the sources of energy and industries covered are not comprehensive enough. Although the decision tree model has been utilized for carbon emission prediction and emission reduction analysis, the issues of overfitting and the model’s challenge in accounting for the synergistic effects of multiple factors have hindered its practical application performance.

Moreover, although the impact of regional heterogeneity on carbon emissions has received attention in the aforementioned studies, there is a lack of research on the coupling effects of carbon emissions caused by the consumption of different energy categories across different regions and industries.

In order to conduct a more accurate and in-depth analysis of the interactive effects of energy types and regional disparities on the causes of carbon emissions, an EG-Tree model is proposed in this study, which enhances gradients and regularizes gradient boosting within the framework of a decision tree model, for the purpose of conducting cause analysis of carbon emissions that integrates regional heterogeneity under the coupling effect of multiple factors. The spatial disparities in carbon emission intensities across various regions and industries are capable of being precisely captured by this model. Subsequently, the variations in carbon emissions are examined in relation to nine energy types, namely coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas, as well as seven common geographical divisions prevalent in China. Moreover, the underlying causes are further delved into.

The research approach of this study is as follows. Firstly, a framework based on the decision tree model, in which weak classifiers are trained iteratively and stored in a “Block” format, is first proposed. Each item within every category is assigned a score, and the objective function value, i.e., the score of the tree, is the sum of the scores of all leaf nodes. The larger the value, the stronger the data correlation. Subsequently, data on the total consumption of nine energy sources, including coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas, were collected, alongside data on the total carbon emissions from six industries as follows: the transportation and construction industry, industrial sector, agriculture and forestry industry, resource recycling industry, purchased electricity industry, and the heating and cooling industry. Next, the intensity of the impact of energy sources on carbon emissions across various industries, as well as the regional heterogeneity contributing to carbon emissions in different industries, is analyzed by the EG-Tree model. An EG-Tree model approach based on a decision tree framework that integrates gradient boosting and regularization techniques is proposed in this study, which is capable of accurately capturing the spatial variability in carbon emissions across different energy sources and regions. The practical significance of the EG-Tree model lies in its capacity to establish a multi-policy coordination framework through precise carbon control in high-emission sectors, the design of differentiated energy transition pathways, and the optimization of carbon accounting systems, thus offering scientific decision-making support for achieving efficient emission reductions.

2. Model Construction

2.1. Construction of EG-Tree Model

A special tree model that enhances gradients and incorporates regularized gradient boosting, namely the enhanced gradient tree (EG-Tree) model, was constructed in this study within the framework of the decision tree model. It trains multiple weak classifiers iteratively, optimizes the loss function, and combines the gradient boosting algorithm with regularization techniques to effectively reduce the risk of overfitting. The EG-Tree accomplishes tasks such as classification and multivariate regression based on different activation layers of functions. Compared with traditional decision tree models, it demonstrates higher accuracy and efficiency when processing large-scale data. By exploring the strengths of associations between different impact factors and carbon emissions, it conducts a principal cause analysis of carbon emissions. The basic principle of the EG-Tree model is to pre-sort the impact factors in each column and store them in the cache in Block form. Feature values and gradient statistics are mapped one-to-one based on indices. Every time a node splits, the pre-sorted module is repeatedly invoked, with different features distributed in independent Blocks. Distributed or multi-threaded computation is then performed based on this. The principle of EG-Tree model is shown in Figure 1, and the various numbers shown in the figure each represent a unique feature value.

$$g_i={\displaystyle \frac{\partial L}{\partial F_{m-1}(x_i)}},h_i={\displaystyle \frac{{\partial }^{2}L}{{\partial }^2{F}_{m-1}(x_i)}}$$

(1)

where L represents the loss function (the square of (10,000 tons of carbon dioxide)); i represents the i-th sample; F_m−1(x_i) represents the model’s predicted values from the (m − 1)-th iteration (10,000 tons of carbon dioxide); x_i represents the feature vector of the i-th sample (10,000 tons); g_i represents the first-order derivative (gradient) of the loss function with respect to the current prediction (10,000 tons of carbon dioxide); and h_i represents the second-order derivative (Hessian) of the loss function with respect to the current prediction (the square of (10,000 tons of carbon dioxide)).

By classifying features through the model, a regression tree model is utilized to predict feature values. When F_m−1 is determined, a g_i and an h_i can be calculated for each sample i. The specific calculation process is as shown in Equation (1).

2.2. Impact Factor Importance Scoring Algorithm

When scoring the importance of features, the objective function of the EG-Tree model is aggregated and summed. The objective function is as follows, represented by Equation (2) through (8):

$$V={\displaystyle \sum _{i=1}^N\left[g_i{f}_m(x_i)+\frac{1}{2}{h}_i{f}_m^2(x_i)\right]}+\gamma T+{\displaystyle \frac{1}{2}}\lambda {\displaystyle \sum _{j=1}^T{w}_j^2}$$

(2)

where T is the number of leaf nodes of the tree, and γ, λ are hyperparameters. And f represents the regression function, prediction, and structure of a single tree; w_j represents the regression coefficient of leaf node j; and V represents the impact score; j represents the node.

Then, the regularization term and the empirical risk term are combined, and the sample set on node j is defined as:

$$I(j)=\left\{x_i|q(x_i)=j\right\}$$

(3)

where q(x_i) is the indexing function that maps samples to nodes, I(j) is the set of samples mapped to leaf node j (Set of sample indices) and the regression value on leaf node j is:

$$w_j=f_m(x_i),i\in I(j)$$

(4)

Let:

$${\displaystyle {\sum }_{i\in I(j)}{g}_i}=G_j,{\displaystyle {\sum }_{i\in I(j)}{h}_i}=H_j$$

(5)

where both G and H are functions with respect to j. Then, the objective function is as follows:

$$V={\displaystyle \sum _{i=1}^T\left[G_j{w}_j+\frac{1}{2}(H_j+\lambda )w_j^2\right]}+\gamma T$$

(6)

where V is the score representing the impact degree of this factor on carbon emissions.

Weighted summation is performed on each score within a certain category to obtain the impact factor degree score for that category. At this point, the samples (x_i, y_i, h_i, g_i) within each node are determined values, meaning Gj, H_j, G_j, and T are also determined values. The extreme point of the quadratic function is as shown in Equation (7):

$$w_j^{*}=-{\displaystyle \frac{G_j}{H_j+\lambda }}$$

(7)

where $w_j^{*}$ is the optimal weight for node j (obtained by minimizing the objective function).

The objective function value, which is the score of the tree, is the sum of the scores of all leaf nodes. The larger this value is, the stronger the data correlation is, as shown in Equation (8):

$$V*={\displaystyle \sum _{j=1}^T\left(-\frac{1}{2}\frac{G_j^2}{H_j+\lambda }+\gamma \right)}$$

(8)

where V* is the global aggregated score for the optimal weight $w_j^{*}$ of leaf nodes in the EG-Tree model.

The principle of tree structure scoring is shown in Figure 2.

For the branching principle mechanism of the EG-Tree, in this study, it is designed to be based on feature evaluation. After the total sample is input into the model, the model first identifies the most significant features and then classifies the data based on their characteristics. During the secondary selection process, the data are partitioned based on the next most significant features, with the overall process illustrated in the figure. In the diagram, triangles represent the unidirectional paths for data flow or gradient transmission, while squares denote the physical storage units for feature Blocks. The carbon emission levels are ranked in descending order as red (highest), followed by yellow, and then blue (lowest). Blue triangles correspond to the values g₁ and h₁, blue squares to g₂ and h₂, yellow squares to g₃ and h₃, yellow triangles to g₄ and h₄, and red squares to g₅ and h₅. The overall workflow in Figure 2 proceeds as follows: first, the shape is checked to determine if it is a triangle; if so, it is further evaluated for the color blue—if blue, the output is I₁ = {1}, G₁ = g₁, and H₁ = h₁; if not blue, the output is I₂ = {4}, G₂ = g₄, and H₄ = h₄. If the shape is not a triangle, the output is I₃ = {2, 3, 5}, G₃ = g₂ + g₃ + g₅, and H₃ = h₂ + h₃ + h₅.

2.3. Evaluation of Model Accuracy

To validate the accuracy of the model, comparisons were made in this study between the prediction results generated by the EG-Tree model and the prediction results obtained from the DTR (decision tree regression model), RFR (random forest regression model), GBDT (gradient boosting decision tree model), and Light-GBM (light gradient boosting machine model). The evaluation is conducted using MAE (mean absolute error), RMSE (root mean square error), and MAPE (mean absolute percentage error) metrics, with the relevant formulas provided as follows:

$$MAE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n\left|y_i-{\stackrel{⌢}{y}}_i\right|}$$

(9)

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n{\left(y_i-{\stackrel{⌢}{y}}_i\right)}^2}}$$

(10)

$$MAPE={\displaystyle \frac{100\%}{n}}{\displaystyle \sum _{i=1}^n\left|\frac{y_i-{\stackrel{⌢}{y}}_i}{y_i}\right|}$$

(11)

where i represents the i-th sample, $y_i$ denotes the actual value, ${\stackrel{⌢}{y}}_i$ denotes the predicted value, and n represents the total number of samples.

3. Data Specification

3.1. Data Description

An analysis of the causes of carbon emissions under the coupling effect of multiple factors while considering regional heterogeneity was conducted by this study, based on two panel datasets. The two panel datasets included a provincial carbon emission estimation dataset for the period from 1997 to 2022. The first panel dataset encompasses consumption data for different types of energy across 30 provinces. The total amounts of energy consumed for the nine types of energy sources, including coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas, are presented in

Table 1. Examples of consumption amounts for different types of energy in different provinces.

Province	Year	Coal Consumption (10,000 tons)	Coke Consumption (10,000 tons)	Crude Oil Consumption (10,000 tons)	Gasoline Consumption (10,000 tons)	Kerosene Consumption (10,000 tons)	Diesel Oil Consumption (10,000 tons)	Fuel Oil Consumption (10,000 tons)	Liquefied Petroleum Gas Consumption (10,000 tons)	Natural Gas Consumption (10,000 tons)
Beijing	2020	134.98	0.01	781.77	423.06	457.88	112.55	0.27	19	189.12
	2021	130.78	0	776.43	480.02	496.28	130.68	0.61	20.42	189.96
	2022	79.29	0	774.92	374.82	330.32	125.71	0.2	17.14	197.95
Tianjin	2020	3745.28	929.37	1394.16	284.73	85.32	325.05	52.61	16.56	117.03
	2021	3428.78	752.06	1722.47	291.12	93.83	338.18	47.23	15.14	123.45
	2022	3314.72	704.72	1660.88	269.19	75.62	340.15	52.08	19.73	127.52

. The second panel dataset comprises provincial carbon emission data by industry from 1997 to 2022, covering total carbon emission data for six industries: the transportation and construction industry, industrial sector, agriculture and forestry industry, resource recycling industry, purchased electricity industry, and the heating and cooling industry, as shown in

Table 2. Carbon emission amounts for different industries in different provinces.

Province	Year	Transportation and Construction Industry (10,000 Tons of Carbon Dioxide)	Industrial Sector (10,000 Tons of Carbon Dioxide)	Agriculture and Forestry Industry (10,000 Tons of Carbon Dioxide)	Resource Recycling Industry (10,000 Tons of Carbon Dioxide)	Purchased Electricity Industry (10,000 Tons of Carbon Dioxide)	Heating and Cooling Industry (10,000 Tons of Carbon Dioxide)
Beijing	2020	11635.97	20054.98	6335.69	3589.84	3749.30	7731.54
	2021	8548.35	18585.80	4741.50	8272.53	3637.01	4151.85
	2022	8574.12	18346.06	7511.46	6035.23	4422.47	3477.19
Tianjin	2020	3088.76	7142.88	1755.09	3404.75	2038.59	2111.04
	2021	3626.45	7657.18	1925.94	3600.56	2324.74	2505.79
	2022	4846.94	7131.17	2416.57	2024.48	2146.97	2557.58

.

3.2. Calculation Method

The carbon emission coefficient method was used to calculate carbon dioxide emissions in this study, which is based on the consumption of various fossil fuels. Calculations were performed using the carbon emission coefficients of fossil fuels provided by the IPCC Guidelines (2006), and the results were obtained in accordance with the research findings of Liu Chuanming [24] and Wang Huiying [25], as shown in Equation (12):

$$CE={\displaystyle {\sum }_{i=1}^9{E}_i}\times NC{V}_i\times CE{F}_i$$

(12)

where CE represents the amount of carbon dioxide emissions (10,000 tons of carbon dioxide); i represents the i-th type of fossil fuel; E_i represents the consumption of the i-th type of fossil fuel (10,000 tons); NCV_i represents the average low calorific value of the i-th type of fossil fuel(GJ/t orGJ/10⁴Nm³); and CEF_i represents the carbon emission coefficient of the i-th type of fossil fuel. Nine types of energy, including raw coal, coke, crude oil, gasoline, kerosene, diesel oil, fuel oil, liquefied petroleum gas, and natural gas, were utilized in this study for the calculation of carbon dioxide emissions, and the carbon emission coefficients corresponding to different types of energy are presented in

Table 3. Carbon emission coefficients of nine energy sources *.

Energy Sources	Average Low Heating Value (kJ/kg)	Standard Coal Coefficient (kgce/kg)	Carbon Content Per Unit of Heat (t-c/TJ)	Carbon Oxidation Rate (%)	Carbon Dioxide Emission Coefficient
Raw coal	20,908	0.7143	26.37	0.94	1.9003 kg∙CO2/kg
Coke	28,435	0.9714	29.42	0.93	2.8604 kg∙CO2/kg
Crude oil	41,816	1.4286	20.08	0.98	3.0202 kg∙CO2/kg
Gasoline	43,070	1.4714	18.9	0.98	2.9251 kg∙CO2/kg
Kerosene	43,070	1.4714	19.6	0.98	3.0179 kg∙CO2/kg
Diesel oil	42,651	1.4571	20.2	0.98	3.0959 kg∙CO2/kg
Fuel oil	41,816	1.4286	21.1	0.98	3.1705 kg∙CO2/kg
Liquefied petroleum gas	50,179	1.7143	17.2	0.98	3.0119 kg∙CO2/kg
Natural gas	38,931	1.3300	15.32	0.99	2.1622 kg∙CO2/kg

* Instructions: 1. A fuel with a low (net) calorific value equal to 29,307 kilojoules (kJ) is defined as 1 kg of standard coal equivalent (1 kgce); 2. The first two columns in the table above are sourced from the “General Principles for Calculation of the Comprehensive Energy Consumption” (GB/T 2589-2008) [26]; 3. The last two columns in the table above are sourced from the “Guidelines for the Preparation of Provincial Greenhouse Gas Inventories” (FGBQ [2011] No. 1041); 4. Calculation method for “carbon dioxide emission coefficient”: Taking “raw coal” as an example, 1.9003 = 20,908 × 0.000000001 × 26.37 × 0.94 × 1000 × 3.66667.

.

4. Experiment and Result Discussion

4.1. Carbon Emission Intensity of Various Industries Considering Regional Heterogeneity

China is typically divided into seven major geographical regions: East China, South China, North China, Central China, Southwest China, Northwest China, and Northeast China based on geographical and natural conditions as well as economic development [27].

4.1.1. Comparison of Prediction Results from Different Models

Taking Eastern China, Northeast China, and Central China as examples, the carbon emission intensity impact factors for the DTR, RFR, GBDT, Light-GBM, and the EG-Tree model were calculated. The MAE, RMSE, and MAPE metrics for different models are presented in

Table 4. The MAE, RMSE, and MAPE metrics for different models.

Eastern China	Performance evaluation
	MAE	RMSE	MAPE
DTR	3425.9135	5005.8092	10.74%
RFR	3050.3819	3936.3953	9.29%
GBDT	2930.8671	3881.3712	8.94%
Light-GBM	2485.6903	3075.4195	7.68%
EG-Tree	2292.7858	3330.7504	6.47%
Northeast China	Performance evaluation
	MAE	RMSE	MAPE
DTR	2462.9956	2998.6893	10.18%
RFR	2353.5125	2782.0036	8.34%
GBDT	2473.5052	2917.3763	8.83%
Light-GBM	2456.0197	3081.107	7.94%
EG-Tree	2164.8509	2643.0878	7.90%
Central China	Performance evaluation
	MAE	RMSE	MAPE
DTR	4443.9273	5396.3621	17.08%
RFR	3329.2644	4987.0962	12.81%
GBDT	3660.2287	4957.0896	13.48%
Light-GBM	4216.9413	5654.2967	17.84%
EG-Tree	2879.325	6721.628	9.22%

.

In the three scenarios of Eastern China, Northeast China, and Central China, the MAE values for the EG-Tree model were 2292.7858, 2164.8509, and 2879.325, respectively; the RMSE values were 3330.7504, 2643.0878, and 6721.628, respectively; and the MAPE values were 6.47%, 7.90%, and 9.22%, respectively. As can be seen from the above data, the data prediction accuracy of the EG-Tree model proposed in this study is relatively high.

4.1.2. Impact Factors of Carbon Emission Intensity in Different Regions Across Various Industries Quantified Using the EG-Tree Model

The impact factors of carbon emission intensity in different regions across various industries were quantified using EG-Tree model. It was found that there are significant spatial differences in carbon emission intensity among different regions within the same industry and among different industries within the same region. A heat map generated using the Geographic Information System (GIS) illustrates the regional disparities in carbon emissions across various industries, with factors represented on the vertical axis and different colors indicating the intensity of influence, as shown in Figure 3 (The gray areas in the figure represent missing relevant data). The causes of carbon emissions under the coupling effect of multiple factors based on regional heterogeneity were analyzed in this study.

The following conclusions were drawn from Figure 3.

(1) The total impact factors of carbon emission intensity in different regions, rank from highest to lowest, are East China, Northwest China, Southwest China, North China, Central China, Northeast China, and South China. East China and North China, which are economically more developed and have the highest energy consumption nationwide, have relatively high total carbon emissions, accounting for 26.50% and 15.76% of the national total carbon emissions, respectively, thus resulting in significant carbon emission pollution. In contrast, Northeast China and Central China have lower total carbon emission intensities, with total carbon emissions accounting for 10.66% and 10.68% of the national total, respectively, due to lower energy consumption levels.

In high-emission regions such as East China and North China, a cross-provincial collaborative mechanism for clean energy should be established. By leveraging East China’s technological advantages in offshore wind power and North China’s abundant photovoltaic resources, the promotion of distributed renewable energy to replace coal-fired power generation can be achieved. Northeast China and Central China should develop smart energy systems on the basis of consolidating their existing energy advantages. In Northeast China, it is recommended to expand the scale of wind power and photovoltaic installations, along with supporting energy storage facilities. Meanwhile, pilot projects of “integrating wind, photovoltaic, thermal, and energy storage” should be carried out to gradually reduce the proportion of thermal power generation. Central China boasts abundant hydropower resources, so it is suggested to expand the scale of power transmission from the Three Gorges Hydropower Station, with Hubei and Hunan as the cores, and support it with distributed photovoltaic and energy storage installations, thereby forming a low-carbon power grid based on hydropower and supplemented by new energy for peak regulation.

(2) The total impact factors of carbon emission intensity vary across different industries, rank from largest to smallest as follows: purchased electricity industry, resource recycling industry, agriculture and forestry industry, heating and cooling industry, transportation and construction industry, and the industrial sector. The total carbon emissions across different industries are as follows: the industrial sector emits 61,318,924,900 tons of CO₂, the transportation and construction industry emit 33,813,445,500 tons of CO₂, the resource recycling industry emits 20,773,558,000 tons of CO₂, the agriculture and forestry industry emit 20,285,160,100 tons of CO₂, the purchased electricity industry emits 15,847,229,000 tons of CO₂, and the heating and cooling industry emit 15,570,215,000 tons of CO₂. The industrial sector and the transportation and construction industry account for a relatively large proportion of total carbon emissions, representing 36.58% and 20.17% of the national total carbon emissions, respectively, while the purchased electricity industry and the heating and cooling industry account for a relatively small proportion, representing 9.45% and 9.29% of the national total, respectively.

In the industrial sector, priority should be given to promoting the cleanliness of the energy structure, accelerating the process of replacing coal-fired power, and achieving direct supply of electricity from renewable energy sources to high-energy-consuming enterprises through smart grids. This could be achieved by establishing a cross-regional alliance for direct green energy electricity supply, and implementing a mechanism of “linking carbon emission intensity with electricity pricing”, imposing surcharges on enterprises using high-emission electricity to thereby encourage the increased use of clean energy by grid-related enterprises.

(3) The carbon emissions of various industries in East China ranked highest nationwide, with the industrial sector and the transportation and building sector being major contributors, accounting for 36.20% and 20.09% of the total carbon emissions of all industries in this region, respectively. In North China, the carbon emissions of various industries are also substantial, with the industrial sector and the transportation and building sector again being significant, representing 36.93% and 20.06% of the total carbon emissions of all industries in the region, respectively. In Northeast China, the carbon emissions of various industries are all at a relatively low level nationwide. Specifically, the heating and cooling sector as well as the purchased electricity sector have relatively small carbon emissions, accounting for 8.75% and 9.58% of the total carbon emissions of all industries in this region, respectively. In Central China, the carbon emissions of various industries are also relatively low, with particularly low emissions in the aforementioned two sectors, accounting for 8.87% and 9.53% of the total carbon emissions of all industries in this region, respectively.

Although the overall carbon emissions are relatively low in Northeast China and Central China, the carbon emission issues in the heating and cooling sector and the purchased electricity sector still require attention. Through cross-regional cooperation and by learning from the experiences of East China and North China, we can promote the low-carbon transformation of the aforementioned industries.

4.2. A Coupled Analysis of the Diverse Factors Contributing to Carbon Emissions in Various Industries, Taking into Account Regional Heterogeneity

A coupled analysis of these diverse factors was conducted using the EG-Tree model proposed in this study. Figure 4 presents a cause analysis of carbon emission intensities across different industries in various regions, considering the impact of multiple factors. As a data visualization method, it employs color intensity to represent data magnitude, enabling a straightforward illustration of data distribution trends and patterns, with the analysis results showing that:

(1) North China, East China, and Northwest China exhibit a high degree of dependence on energy sources such as coal, coke, crude oil, gasoline, kerosene, diesel oil, and fuel oil, resulting in relatively large carbon emissions with average carbon emission intensity impact factors ranging from 5300 to 7400, whereas they have a lower dependence on natural gas and liquefied petroleum gas, leading to smaller carbon emissions with average impact factors ranging from 2700 to 5100. North China has the highest dependence on coal, with an average factor of 7442. East China has the highest dependence on kerosene, with an average factor of 9819. Northwest China has the highest dependence on fuel oil, with an average factor of 8580.

A targeted carbon quota allocation mechanism should be established based on the identified characteristics of high emission volumes in the eastern region and high emission intensities in the western region. New coal cleaning technologies and energy efficiency enhancement technologies should be integrated in the Northwest region, and intelligent networking technology should be utilized to simulate and improve the energy network layout within the region. The Northwest region may directionally transfer the carbon quotas generated by improving fuel oil efficiency to the heavy industry base in North China, thus forming a closed loop of resource compensation.

(2) The Northeast region has a high degree of dependence on energy sources such as kerosene, fuel oil, coke, and coal, resulting in relatively large carbon emissions, with its average carbon emission intensity impact factors ranging from 5400 to 6800. The Central China region has a high degree of dependence on energy sources such as crude oil and coal, leading to significant carbon emissions, with average impact factors of 6818 and 6802, respectively. The South China region has a high degree of dependence on energy sources such as coke and fuel oil, resulting in substantial carbon emissions, with average impact factors of 7561 and 7162, respectively. The Southwest region has a high degree of dependence on energy sources such as coke and coal, causing considerable carbon emissions, with average impact factors of 9070 and 8758, respectively.

Each region should formulate strategies targeting its own energy and carbon emission issues. The Northeast region needs to further promote coal clean reuse technology and widely popularize carbon capture technology for coal-based energy. The Central China region should screen industries with high added value and low energy consumption. The South China region should make use of its coastal advantages to establish offshore power generation and tidal energy projects. To address the spatial spillover effect of carbon emissions, the Southwest region should establish an ecological compensation mechanism with the eastern region, facilitating the development of renewable energy through the transfer of funds and technology.

(3) All industries have a relatively high degree of dependence on coal, coke, kerosene, and fuel oil, resulting in large carbon emissions, with average impact factors of 7140, 7217, 6610, and 7310, respectively.

Regarding coke, which contributes to high carbon emission factors, coke oven gas capture and purification technology should be researched and developed, and the traditional coking process should be ungraded into a closed-loop system of “coke making—gas power generation—carbon capture” to achieve internal energy circulation. A clean energy coupling system should be developed centered around kerosene, and through the co-processing technology of coal and kerosene, the coordinated conversion and clean utilization of coal and heavy oil should be achieved.

An analysis on the correlation between energy consumption in different regions and carbon emission intensity across various industries was carried out. However, the potential causal relationship between these variables still requires further examination through additional research, which should be noted.

4.3. Model Error Analysis

For different regions and industries, the RMSE (root mean square error) values of the EG-Tree model are shown in

Table 5. Model fitting RMSE values for carbon emission intensity in various industries across different regions.

RMSE	Transportation and Construction Industry	Industrial Sector	Agriculture and Forestry Industry	Resource Recycling Industry	Purchased Electricity Industry	Heating and Cooling Industry
East China	0.217	0.358	0.088	0.257	0.786	0.192
North China	0.529	0.621	0.232	0.409	0.419	0.570
Central China	0.404	0.448	0.118	0.223	0.226	0.102
Northwest China	0.173	0.248	0.141	0.230	0.134	0.294
South China	0.483	0.453	0.297	0.420	0.333	0.288
Northeast China	0.408	0.351	0.290	0.572	0.283	0.224
Southwest China	0.435	0.460	0.167	0.275	0.145	0.191

. Overall, all the root mean square errors are relatively low, ranging from 0.088 to 0.786, indicating a high overall fitting degree of the model.

5. Conclusion and Policy Recommendations

5.1. Conclusions

The panel data on the consumption of different energy types and carbon emissions from different industries in 30 provinces of China from 1997 to 2022 were utilized in this study. A framework based on the decision tree model was proposed in this study, data on the total consumption of nine types of energy and the total carbon emissions of six industries were collected, and the intensity of the impact of various energy sources on carbon emissions in different industries, as well as the factors contributing to regional heterogeneity in carbon emissions across different industries, were analyzed through the EG-Tree model. The study found the following:

(1)

The EG-Tree model constructed in this study combined multiple weak classifiers through the gradient boosting method and introduced a regularization term to prevent model overfitting based on the decision tree model. In the task of achieving associated feature analysis, compared with the decision tree model, this model can better alleviate the overfitting problem and accurately identify the main impact factors leading to carbon emissions. The average model fitting precision of the EG-Tree model, as well as the degree of closeness between its predicted values and the carbon emission intensity values calculated using the carbon emission measurement dataset, was 0.30;

(2)

There are spatial differences in the distribution of carbon emissions across different regions, mainly influenced by factors such as regional economic development characteristics, industrial structure, natural climate, regional development strategies, and energy types. The total carbon emissions in East China and North China are relatively large, while the total carbon emission intensity in Northeast China and Central China is relatively small;

(3)

Industrial sector and transportation and construction industry have relatively large carbon emissions, accounting for 36.58% and 20.17% of the total national carbon emissions, respectively, while the purchased electricity industry and heating and cooling industry have relatively smaller shares at 9.45% and 9.29%, respectively;

(4)

Both East China and North China have relatively large carbon emissions in the industrial sector and transportation and construction industry, accounting for 36.20%, 20.09% and 36.93%, 20.06% of the total carbon emissions of all industries in these regions, respectively; Northeast China and Central China have relatively small carbon emissions in the heating and cooling industry and purchased electricity industry, accounting for 8.75%, 9.58% and 8.87%, 9.53% of the total emissions of all industries in these regions, respectively.

(5)

North China, East China, and Northwest China have a relatively high degree of dependence on energy sources such as coal, coke, crude oil, gasoline, kerosene, diesel oil, and fuel oil, resulting in significant carbon emissions, with their average carbon emission intensity impact factors exceeding 5300. All regions exhibit a relatively low degree of dependence on energy sources such as natural gas and liquefied petroleum gas, leading to smaller carbon emissions, with average impact factors below 5100. The high-dependency energy sources vary across Northeast China, Central China, South China, and Southwest China;

(6)

Regional carbon emissions are strongly correlated with the energy structure, with dependence on traditional energy sources being the core issue. High carbon emissions in East China and North China stem from their reliance on coal and kerosene (the average carbon emission intensity impact factor for coal in North China was 7442). Northwest China rank second in total carbon emissions due to its dependence on fuel oil (the average carbon emission intensity impact factor for fuel oil in Northwest China was 8580). Although Southwest China has a relatively high proportion of renewable energy, its dependence on coke and coal still drive up carbon emissions in various industries;

(7)

In the southern region of Southwest China, due to the high proportion of hydropower, the intensity of power-related carbon emissions is the lowest. However, the overall average impact factor of carbon emission intensity in the purchased electricity industry remained relatively high at 7290, reflecting the complexity of cross-regional energy allocation and the correlation between regional energy structure and carbon emissions.

This study enables relevant departments to formulate targeted policies and measures to reduce carbon emissions and promote sustainable development through precise analysis of the impacts of different factors in various regions on carbon emissions.

5.2. Policy Recommendations

The following policy recommendations are put forward for urban carbon emission reduction based on the regional differences in carbon emissions across different industries and the carbon emission intensity impact factors obtained through the multivariate factor coupling analysis using the EG-Tree model proposed in this study:

(1)

Concentrate on high-emission industries and carry out precise carbon control strategies. In the industrial industry, it is necessary to accelerate the cleanliness of the energy structure, promote direct connections between high-energy-consuming enterprises and renewable energy power generation, and establish a linkage mechanism for electricity prices. Penalty electricity rates should be imposed on enterprises using high-emission power to compel the use of clean energy. The transportation and construction industry should promote electrification technologies and, in combination with the differences in regional power carbon emission factors, guide high-energy-consuming links to shift towards low-carbon power regions;

(2)

Differentiated energy transformation paths should be adopted to break the inertia of resource dependence. Regions dependent on coal (such as North China and Southwest China) need to promote the upgrading of clean coal technologies. North China should focus on developing coal clean reuse and carbon capture technologies, while Southwest China should introduce funds and technologies through ecological compensation mechanisms to reduce dependence on coke and coal. Fuel oil-dependent regions (such as South China and Northwest China) can develop alternative projects like offshore wind power and tidal energy to reduce fuel oil consumption;

(3)

Improve the data support and regulatory system to enhance the accuracy of carbon accounting. Establish a nationally unified energy digital intelligent platform to dynamically integrate power generation data from thermal power, wind power, photovoltaic power, etc., and optimize inter-provincial power dispatching in combination with regional power grid carbon emission factors;

(4)

Coordinate international experience with regional practice to promote policy innovation. By drawing on the European carbon market and green certificate trading mechanism, explore the “Chinese-style collaborative trading model of green certificates and carbon allowances” to enhance enterprises’ motivation for low-carbon transformation. Pilot demonstration projects for coal substitution and clean energy transformation should be first carried out in pilot regions such as Northwest China and Northeast China, so as to form replicable technical and managerial experiences.

Through the aforementioned policy recommendations, it is possible to effectively balance regional development disparities and industry emission reduction demands, thereby promoting the precise implementation of China’s “dual carbon” goals.