2.4.2. Construction of the GTWR Model
In this study, the decoupling index between economic growth and carbon emissions in the YRB is adopted as the explained variable of the model, while five factors—per capita GDP, urbanization rate, industrial structure upgrading, urban construction land area, and the number of green patent grants—are selected as explanatory variables. Geographically and Temporally Weighted Regression (GTWR) models are constructed for four respective years: 2010, 2014, 2018, and 2022.
Prior to the implementation of the GTWR model, diagnostic tests for correlation and multicollinearity were performed on all candidate variables. The Pearson correlation coefficients (
Table 4) indicate that each of the five selected explanatory variables is significantly correlated with the dependent variable. The variance inflation factor (VIF) estimates (
Table 5) are all below the threshold of 7.5, suggesting the absence of severe multicollinearity among the independent variables. These preliminary diagnostics confirm that the dataset satisfies the necessary preconditions for the subsequent GTWR estimation. In addition, the Gaussian kernel was selected as the kernel function, with the fixed bandwidth determined as 0.115 based on the cross-validation (CV) criterion. The standard Euclidean distance was employed as the distance metric, and local weighted least squares was applied for coefficient estimation.
To determine whether the GTWR model is more appropriate than alternative regression specifications for analyzing the drivers of the decoupling index, this study constructs three models based on the selected variables using SPSS 26.0 and ArcGIS 10.8: ordinary least squares (OLS), geographically weighted regression (GWR), and geographically and temporally weighted regression (GTWR). The parameter estimates of the three models are then compared to identify the specification that yields the best fit. In the regression analysis, the coefficient of determination (R
2), adjusted R
2, and the Akaike information criterion (AICc) are employed as indicators of model goodness-of-fit. The estimation results (
Table 6) show that the GTWR model outperforms the other two across all these metrics, indicating its superior explanatory power for the driving factors and greater reliability of the estimated coefficients. Accordingly, this study adopts the GTWR model to examine the spatiotemporal heterogeneity of the effects of each independent variable on the carbon emission decoupling index.
The specific expression of the model is as follows:
In the formula, represents the i-th sample city; represents the carbon emission decoupling index of the i-th sample city; is the intercept term, denotes the spatiotemporal coordinates of the i-th sample city; , , , , represent per capita GDP, urbanization rate, industrial structure upgrading, urban construction land area, and the number of green patent grants, respectively; are the regression coefficients corresponding to the above independent variables for the i-th sample city, in that order; and is the random error term of the i-th sample city.
2.4.3. Construction of the LEAP-YRB v5 Integrated Assessment Model
This study constructs the LEAP-YRB v5 integrated assessment model to conduct medium- and long-term projections of energy consumption and carbon emissions for the nine provinces of the YRB over the period from 2022 to 2060. The model draws upon the conceptual framework of the Long-range Energy Alternatives Planning (LEAP) system but adopts a hybrid macro-sectoral-driven approach that is more suitable for regional macro-level forecasting. This approach treats macroeconomic indicators (GDP) as the core driving force of total energy demand, while incorporating the dynamic evolution of sectoral structures and inter-provincial heterogeneity parameters to achieve a refined simulation of the complex energy system.
The core framework of the LEAP-YRB v5 model consists of multiple interrelated modules (
Figure 3).
This model adopts the macroeconomic energy intensity method to forecast total energy demand. Based on the dynamically changing share of energy consumption in each sector, the total energy demand is allocated to six end-use sectors. For any province
p in year t, the calculation formula for total energy demand is as follows:
In the formula, is the total energy demand of province p in year t; is the gross regional product of province p in year t; is the energy intensity per unit GDP of province p in year t; and is the industrial structure adjustment factor.
Total demand is then allocated to six end-use sectors—industry, transportation, residential life, construction, commercial and services, and primary industry—using province-specific baseline shares and dynamic adjustment parameters. The sectoral demand is further allocated to ten energy types: raw coal, coke, crude oil, gasoline, diesel, fuel oil, natural gas, liquefied petroleum gas, electricity, and heat. Inter-provincial adjustment coefficients modify the national sector-energy matrix to reflect coal dependence in Shanxi and Inner Mongolia and hydropower advantages in Sichuan and Qinghai.
- 2.
Carbon Emission Accounting Method
Total carbon emissions consist of direct final-energy emissions from fossil fuel combustion and indirect emissions from electricity and heat consumption (
Table 7).
In the formula, is the consumption of fuel f; is the lower heating value; is the carbon content per unit calorific value; is the carbon oxidation rate; and 44/12 is the molecular weight ratio for converting carbon to carbon dioxide.
- 3.
Inter-Provincial Heterogeneity Design
Economic Growth Pathway: Differentiated GDP growth rates are set for each province under different scenarios.
Sectoral Energy Consumption Structure: Based on provincial statistical data, a unique sectoral energy consumption share structure is established for each province.
Energy Type Structure: Inter-provincial adjustment coefficients are introduced to adjust the baseline national average sector-energy type matrix, so as to reflect the high dependence on coal in provinces such as Shanxi and Inner Mongolia, as well as the abundant hydropower resource characteristics of provinces such as Sichuan and Qinghai.
- 4.
Model Validation and Evaluation
Taking 2022 as the base point, the parameters under the baseline scenario are used to backcast energy consumption and carbon emissions from 2016 to 2021, which are then compared with historical statistical data. The Mean Absolute Percentage Error (MAPE) is adopted as the evaluation indicator:
In the formula, is the historical actual value, and is the model predicted value.
- 5.
Key Parameter Assumptions and Scenario Settings
To explore the energy transition and carbon emission trajectories of the YRB under different development pathways, this study designs five scenarios (
Table 8): the Business-as-Usual scenario (BAU), the Policy-Driven Scenario (PDS), the Energy Efficiency Improvement scenario (EEI), the Clean Energy Scenario (CES), and the Carbon-Neutrality-Oriented Scenario (CS). These scenarios are characterized by different settings of key driving parameters, primarily encompassing macroeconomic conditions, energy efficiency, energy structure, power system decarbonization, and CCUS technology application.
The assumptions underlying all scenario parameters in this study are supported by national top-tier low-carbon and energy policies as well as authoritative domestic and international research reports. The policy benchmarks draw on the Action Plan for Carbon Dioxide Peaking Before 2030 (
https://app.www.gov.cn/govdata/gov/202110/26/477466/article.html, accessed on 12 March 2026), the 14th Five-Year Plan for a Modern Energy System (
https://zfxxgk.nea.gov.cn/2022-01/29/c_1310524241.htm, accessed on 12 March 2026), and the Notice on Greenhouse Gas Emission Reporting and Management for the Power Generation Industry, 2023–2025 issued by the Ministry of Ecology and Environment (
https://www.mee.gov.cn/xxgk2018/xxgk/xxgk06/202302/t20230207_1015569.html, accessed on 12 March 2026), which provide official policy guidance for core constraint indicators including industrial restructuring, energy intensity control, coal consumption substitution and low-carbon power transformation. The technical pathways and medium-to-long-term transition potentials are quantified and validated against the China Carbon Capture, Utilization and Storage Annual Report 2023 (
https://www.acca21.org.cn/trs/000100170002/, accessed on 12 March 2026), the IEA’s An Energy Sector Roadmap to Carbon Neutrality in China (
https://www.iea.org/reports/an-energy-sector-roadmap-to-carbon-neutrality-in-china/executive-summary, accessed on 12 March 2026), and the report Towards Carbon Neutrality: A Study on China’s Long-Term Low-Carbon Transition Pathways and Strategies released by the Institute of Climate Change and Sustainable Development, Tsinghua University (
https://lce.tsinghua.edu.cn/info/1010/1307.htm, accessed on 12 March 2026). These studies offer quantitative evidence for exploratory scenario parameters covering energy efficiency improvement, electrification expansion, large-scale CCUS deployment and long-term evolution of the energy system. All scenario configurations fully align with China’s established dual-carbon targets, industrial regulatory standards and state-of-the-art quantitative research on low-carbon transitions, ensuring the rationality of policy orientation and academic robustness of all parameter settings.
- 6.
Multi-temporal Sensitivity and Monte Carlo Simulation
This study adopts an uncertainty assessment framework combining multi-temporal single-factor sensitivity analysis and Monte Carlo simulation. The two methods complement each other with distinct functions: sensitivity analysis reveals the mechanism of parameter impacts, while Monte Carlo simulation quantifies the probabilistic fluctuation of outputs, jointly achieving a comprehensive uncertainty evaluation of the carbon emission prediction model.
The multi-temporal single-factor sensitivity analysis individually perturbs key parameters—including GDP, energy intensity, coal share, power emission factors, and CCUS—with gradient disturbance ratios, and calculates the percentage changes in carbon emissions across multiple periods from 2030 to 2060, thereby identifying the core variables that exert the most prominent impacts on emission outputs and clarifying the temporal evolution characteristics of the independent effect of each single parameter. Nevertheless, this method can only examine local single-variable effects and fails to reflect the comprehensive risks induced by simultaneous fluctuations of multiple parameters.
The Monte Carlo simulation assigns triangular probability distributions to all parameters and performs 1000 independent random samplings for each scenario. It then uses the 2.5th–97.5th percentile ranges and median values derived from the sampling results to quantify the global uncertainty range of carbon emissions under the coupling of all parameters.