Quantitative simulation and validation of energy carbon emission efficiency changes in Chinese urban agglomerations

In the context of the global energy dilemma, enhancing energy efficiency has inevitably become a pivotal strategy for mitigating energy waste and promoting sustainable development. Urban agglomerations, as growth poles leading high-quality regional economic development, play a significant role in this process. Within these urban agglomerations, the aggregation of various factors and the substitution of energy resources substantially influence the energy carbon emission efficiency (ECEE) of surrounding cities during their development and maturation phases. This study initially employs a three-stage Data Envelopment Analysis (DEA) to quantitatively analyze the ECEE values of 19 urban agglomerations from 2006 to 2020. It then establishes a methodology for calculating the joint intensity (JI) and joint threshold (JT) of ECEE within these urban agglomerations. Finally, a validation process is executed using MATLAB simulation and verification methodology to fit and authenticate the evolutionary patterns of ECEE in Chinese urban agglomerations. The primary objective of this research is to model the evolution of ECEE, thereby exploring the sustainable development pathways for urban agglomerations in China. The research findings indicate that: (1) The results from the three-stage DEA demonstrate that, after removing the influences of external environmental factors and random errors, the comprehensive technical efficiency (TE) of energy carbon emissions for the 19 urban agglomerations in China experienced a wave-like increase, rising from 0.410 to 0.506 between 2006 and 2020. (2) The calculation results of the constructed JI model indicate that the JT values of ECEE for national-level, regional-level, and local-level urban agglomerations are 1006.92, 226.60, and 160.14, respectively. The national-level urban agglomerations have significantly higher JT values and JI than the other two levels of urban agglomerations. (3) The results of the Matlab simulation verification show that 16 urban agglomerations fit well with the wave-like ascending evolutionary pattern. However, four urban agglomerations exhibit an opposite fitting effect due to the influence of their pillar industries or the small number of cities within these accumulations, making them unrepresentative. Consequently, the evolutionary curve of ECEE in Chinese urban agglomerations generally exhibits a wave-like upward trend over time.