The characteristics of cloud fractal dimension in shallow cumulus clouds and their implications to cloud processes

Shallow cumulus clouds critically influence Earth's climate and hydrological cycles. Yet, their simulation remains uncertain in climate models, partly due to idealized geometric assumptions that neglect turbulent boundary irregularities.

To overcome this limitation, this study explores irregularity of cloud lateral ‑boundary using fractal dimension. The fractal dimensions were calculated using the Area‑Perimeter method (characterizing statistical self‑similarity of the cloud field) and the Box‑Counting method (capturing the irregularity of individual clouds). The results show that the fractal dimension derived from the Box‑Counting method is consistently higher than that from the Area‑Perimeter method, indicating that most clouds are not strictly self‑similar structures. A significant positive correlation is found between fractal dimension and precipitation intensity suggesting relationships between cloud morphology and cloud processes. Furthermore, the adiabaticity of cloud was quantified by computing the distribution differences of conserved quantities between the cloud interior and its surroundings. 

These findings highlight that incorporating realistic cloud‑boundary geometry into parameterizations can better represent turbulent mixing and cloud‑environment interactions, ultimately contributing to more accurate simulations of shallow cumulus evolution.