Fractal Dimension of Shallow Cumulus Cloud Boundaries Beyond Bulk Fractal Scaling

Abstract

Abstract Cloud boundaries reflect turbulent mixing and cloud–environment interactions, but their geometric complexity remains poorly quantified. Here, we investigate the complexity of shallow cumulus cloud edge using two fractal approaches: the bulk area–perimeter method and the individual‐cloud box‐counting method. Using large‐eddy simulations, we find that the box‐counting dimension better captures boundary complexity by resolving cloud‐scale irregularities, whereas the bulk dimension smooths individual morphological variability. Larger clouds exhibit higher box‐counting dimensions and increased deviations from idealized stochastic self‐similar scaling, indicating increasing boundary heterogeneity with cloud size and shape complexity. Wind induces scale‐dependent morphological responses, smoothing small clouds while enhancing boundary complexity in larger clouds through competing dynamical effects. Moreover, box‐counting dimension shows a stronger association with precipitation‐related properties, suggesting a closer link between boundary evolution and cloud processes. These results highlight individual‐cloud fractal analysis as a useful framework for quantifying shallow cumulus complexity and its environmental controls.