A quantitative simulation and verification of the sustainable and low-carbon development efficiency curves for Beijing-Tianjin-Hebei urban agglomeration

The Beijing-Tianjin-Hebei urban agglomeration (BTHUA) has experienced ecological and environmental issues due to its rapid development and expansion, including air and water pollution. Examining inter-regional plans for sustainable and low-carbon sustainable development is crucial and practical for achieving ecological balance among regions and fostering the BTHUA's commitment to collaborative innovation. This study applies the three-stage data envelopment analysis (DEA) model to 13 cities in the BTHUA between 2007 and 2020 to compute the sustainable and low-carbon development efficiency (SLE) and index, and then constructs a fundamental model of urban agglomeration growth. In this study, MATLAB software was used to predict the general evolution trend and development curve for the BTHUA's low-carbon and green economy development. The results of the study indicate (1) the efficiency of sustainable and low-carbon development in the BTHUA has a wave-like ascending tendency, generating an overall development pattern that is centred on core cities and eventually descends toward the periphery. (2) In recent years, coordination between sustainable and low-carbon development indices and development levels within BTHUA has largely improved; however, a changing nonlinear relationship exists between the sustainable and low-carbon efficiency index and development levels. (3) The BTHUA's sustainable and low-carbon development curve displays a tendency that is consistent with the function model's anticipated evolution trend.