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Urbanization and the release of carbon emission are two significant features of contemporary economic and social progress in China. However, there are few studies that consider how urbanization policy goals affect carbon emission. This paper aims to study the nonlinear effects of urbanization policy goals on carbon emission in 13 cities of the Beijing-Tianjin-Hebei region. In this paper, a multi-dimensional spatial disturbance grey model is proposed. Based on matrix perturbation theory, this paper explores the spatial perturbation bounds of the novel model and verifies that the spatial property of the model is consistent with the viewpoint of the First Law of Geography. Then, the novel model is used to predict the urban carbon emission under different urbanization policy goal scenarios. The results showed that the novel model has spatial regional correlation in spatial region prediction. With the development of urbanization level, carbon emissions show a downward trend in more than 50% of cities from 2022 to 2025. In addition, the improvement of urbanization policy goals will promote the carbon peak time of most cities. The carbon emission intensity will exhibit an inverted U-shaped trend distribution in space. The research results are conducive to providing scientific guidance for the formulation of new-type urbanization policies and helping to achieve the dual carbon goals. • A multi-dimensional spatial disturbance grey model is proposed. • The novel grey model is consistent with the viewpoint of the First Law of Geography. • The spatial distribution of carbon intensity showed an inverted U-shaped pattern. [ABSTRACT FROM AUTHOR]