A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales

Abstract

The deterministic motions of clouds and turbulence, despite their chaotic nature, have nonetheless been shown to follow simple statistical power-law scalings: A fractal dimension D relates individual cloud perimeters p to a measurement resolution, and turbulent fluctuations scale with the air parcel separation distance through the Hurst exponent, H. However, it remains uncertain whether atmospheric turbulence is best characterized by a split isotropy that is three-dimensional (3D) with HCombining double low line1/3 at small scales and two-dimensional (2D) with HCombining double low line1 at large scales or by a wide-range anisotropic scaling with an intermediate value of H. Here, we introduce an "ensemble fractal dimension"De-analogous to D-that relates the total cloud perimeter per domain area P as seen from space to the measurement resolution, and we show theoretically how turbulent dimensionality and cloud edge geometry can be linked through HCombining double low lineDe-1. Observationally and numerically, we find the scaling Deg1/45/3 or Hg1/42/3, spanning 5 orders of magnitude of scale. Remarkably, the same scaling relationship links two "limiting case"estimates of P evaluated at resolutions corresponding to the planetary scale and the Kolmogorov microscale, which span 10 orders of magnitude. Our results are nearly consistent with a previously proposed "23/9D"anisotropic turbulent scaling and suggest that the geometric characteristics of clouds and turbulence in the atmosphere can be easily tied to well-known planetary physical parameters.