Kardar-Parisi-Zhang model for the fractal structure of cumulus cloud fields

Abstract

We model the ascent of warm, moist air in the Earth's atmosphere by turbulent convection and expansion with the KPZ equation, familiar in the physics literature on surface growth. Clouds form in domains where the interface between the rising air and its surrounding air achieves an elevation higher than that necessary for condensation. The model predictions are consistent with the perimeter fractal dimension and the cumulative frequency-size distribution of cumulus cloud fields observed from space.